{"id":15,"date":"2025-08-16T10:17:51","date_gmt":"2025-08-16T03:17:51","guid":{"rendered":"https:\/\/solio.online\/blog\/?p=15"},"modified":"2025-11-23T06:08:42","modified_gmt":"2025-11-22T23:08:42","slug":"cac-phuong-trinh-lien-quan-den-hat-trung-phan-tich-tu-co-ban-den-nang-cao","status":"publish","type":"post","link":"https:\/\/solio.online\/blog\/cac-phuong-trinh-lien-quan-den-hat-trung-phan-tich-tu-co-ban-den-nang-cao\/","title":{"rendered":"C\u00e1c Ph\u01b0\u01a1ng Tr\u00ecnh Li\u00ean Quan \u0110\u1ebfn H\u1ea1t Trung \u2013 Ph\u00e2n T\u00edch T\u1eeb C\u01a1 B\u1ea3n \u0110\u1ebfn N\u00e2ng Cao"},"content":{"rendered":"\n<p class=\"wp-block-paragraph\"><strong>Gi\u1edbi Thi\u1ec7u<\/strong><\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Trong l\u00fd thuy\u1ebft m\u1edbi v\u1ec1 h\u1ea1t Trung, ch\u00fang ta gi\u1ea3 \u0111\u1ecbnh r\u1eb1ng photon kh\u00f4ng ph\u1ea3i l\u00e0 c\u00e1c h\u1ea1t di chuy\u1ec3n trong kh\u00f4ng gian m\u00e0 th\u1ef1c ch\u1ea5t ch\u1ec9 l\u00e0 nh\u1eefng dao \u0111\u1ed9ng truy\u1ec1n qua m\u00f4i tr\u01b0\u1eddng n\u1ec1n (h\u1ea1t Trung). M\u00f4i tr\u01b0\u1eddng n\u00e0y kh\u00f4ng ph\u1ea3i l\u00e0 ch\u00e2n kh\u00f4ng r\u1ed7ng, m\u00e0 l\u00e0 m\u1ed9t m\u1ea1ng l\u01b0\u1edbi h\u1ea1t v\u00f4 h\u00ecnh c\u00f3 m\u1eb7t trong to\u00e0n b\u1ed9 v\u0169 tr\u1ee5. D\u01b0\u1edbi \u0111\u00e2y l\u00e0 c\u00e1c ph\u01b0\u01a1ng tr\u00ecnh quan tr\u1ecdng li\u00ean quan \u0111\u1ebfn h\u1ea1t Trung, t\u1eeb c\u00e1c m\u00f4 h\u00ecnh c\u01a1 b\u1ea3n \u0111\u1ebfn c\u00e1c ph\u01b0\u01a1ng tr\u00ecnh ph\u1ee9c t\u1ea1p h\u01a1n trong v\u1eadt l\u00fd l\u00fd thuy\u1ebft.<\/p>\n\n\n\n<figure class=\"wp-block-image size-large\"><img loading=\"lazy\" decoding=\"async\" width=\"683\" height=\"1024\" src=\"https:\/\/cdn.solio.online\/trungglobal-assets\/posts\/core\/blog\/uploads\/2025\/08\/phuong-trinh-hat-Trung-683x1024.webp\" alt=\"C\u00e1c Ph\u01b0\u01a1ng Tr\u00ecnh Li\u00ean Quan \u0110\u1ebfn H\u1ea1t Trung \u2013 Ph\u00e2n T\u00edch T\u1eeb C\u01a1 B\u1ea3n \u0110\u1ebfn N\u00e2ng Cao\" class=\"wp-image-1389\" srcset=\"https:\/\/solio.online\/blog\/wp-content\/uploads\/2025\/08\/phuong-trinh-hat-Trung-683x1024.webp 683w, https:\/\/solio.online\/blog\/wp-content\/uploads\/2025\/08\/phuong-trinh-hat-Trung-200x300.webp 200w, https:\/\/solio.online\/blog\/wp-content\/uploads\/2025\/08\/phuong-trinh-hat-Trung-768x1152.webp 768w, https:\/\/solio.online\/blog\/wp-content\/uploads\/2025\/08\/phuong-trinh-hat-Trung.webp 1024w\" sizes=\"auto, (max-width: 683px) 100vw, 683px\" \/><figcaption class=\"wp-element-caption\"><em>C\u00e1c Ph\u01b0\u01a1ng Tr\u00ecnh Li\u00ean Quan \u0110\u1ebfn H\u1ea1t Trung \u2013 Ph\u00e2n T\u00edch T\u1eeb C\u01a1 B\u1ea3n \u0110\u1ebfn N\u00e2ng Cao<\/em><\/figcaption><\/figure>\n\n\n\n<p class=\"wp-block-paragraph\"><strong>1. Ph\u01b0\u01a1ng Tr\u00ecnh Maxwell \u2013 C\u01a1 S\u1edf C\u1ee7a L\u00fd Thuy\u1ebft \u0110i\u1ec7n T\u1eeb<\/strong><\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Ph\u01b0\u01a1ng tr\u00ecnh Maxwell m\u00f4 t\u1ea3 c\u00e1ch m\u00e0 s\u00f3ng \u0111i\u1ec7n t\u1eeb (bao g\u1ed3m \u00e1nh s\u00e1ng) lan truy\u1ec1n trong kh\u00f4ng gian v\u00e0 \u0111\u01b0\u1ee3c coi l\u00e0 n\u1ec1n t\u1ea3ng c\u1ee7a c\u00e1c ph\u01b0\u01a1ng tr\u00ecnh li\u00ean quan \u0111\u1ebfn h\u1ea1t Trung. Trong m\u00f4 h\u00ecnh n\u00e0y, \u00e1nh s\u00e1ng kh\u00f4ng ph\u1ea3i l\u00e0 m\u1ed9t h\u1ea1t ri\u00eang bi\u1ec7t m\u00e0 l\u00e0 dao \u0111\u1ed9ng trong tr\u01b0\u1eddng \u0111i\u1ec7n v\u00e0 t\u1eeb.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Ph\u01b0\u01a1ng tr\u00ecnh Maxwell c\u00f3 d\u1ea1ng:<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">\\nabla \\cdot \\mathbf{E} = \\frac{\\rho}{\\epsilon_0}, \\quad \\nabla \\cdot \\mathbf{B} = 0<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">\\nabla \\times \\mathbf{E} = -\\frac{\\partial \\mathbf{B}}{\\partial t}, \\quad \\nabla \\times \\mathbf{B} = \\mu_0 \\mathbf{J} + \\mu_0 \\epsilon_0 \\frac{\\partial \\mathbf{E}}{\\partial t}<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Trong \u0111\u00f3:<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>\\mathbf{E} l\u00e0 tr\u01b0\u1eddng \u0111i\u1ec7n,<\/li>\n\n\n\n<li>\\mathbf{B} l\u00e0 tr\u01b0\u1eddng t\u1eeb,<\/li>\n\n\n\n<li>\\rho l\u00e0 m\u1eadt \u0111\u1ed9 \u0111i\u1ec7n t\u00edch,<\/li>\n\n\n\n<li>\\mathbf{J} l\u00e0 d\u00f2ng \u0111i\u1ec7n,<\/li>\n\n\n\n<li>\\epsilon_0 v\u00e0 \\mu_0 l\u00e0 h\u1eb1ng s\u1ed1 \u0111i\u1ec7n t\u1eeb.<\/li>\n<\/ul>\n\n\n\n<p class=\"wp-block-paragraph\">Ph\u01b0\u01a1ng tr\u00ecnh n\u00e0y kh\u00f4ng ch\u1ec9 m\u00f4 t\u1ea3 s\u1ef1 lan truy\u1ec1n s\u00f3ng \u0111i\u1ec7n t\u1eeb trong m\u00f4i tr\u01b0\u1eddng m\u00e0 c\u00f2n l\u00e0 n\u1ec1n t\u1ea3ng l\u00fd thuy\u1ebft cho vi\u1ec7c hi\u1ec3u v\u1ec1 s\u1ef1 truy\u1ec1n s\u00f3ng trong h\u1ea1t Trung.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><strong>2. Ph\u01b0\u01a1ng Tr\u00ecnh S\u00f3ng C\u1ee7a H\u1ea1t Trung<\/strong><\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Trong m\u00f4 h\u00ecnh h\u1ea1t Trung, \u00e1nh s\u00e1ng kh\u00f4ng ph\u1ea3i l\u00e0 m\u1ed9t h\u1ea1t ri\u00eang bi\u1ec7t m\u00e0 l\u00e0 nh\u1eefng dao \u0111\u1ed9ng trong m\u00f4i tr\u01b0\u1eddng n\u1ec1n. T\u1ed1c \u0111\u1ed9 lan truy\u1ec1n c\u1ee7a s\u00f3ng trong m\u00f4i tr\u01b0\u1eddng n\u00e0y ch\u00ednh l\u00e0 v\u1eadn t\u1ed1c \u00e1nh s\u00e1ng. Ph\u01b0\u01a1ng tr\u00ecnh s\u00f3ng cho h\u1ea1t Trung c\u00f3 th\u1ec3 m\u00f4 t\u1ea3 nh\u01b0 sau:<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">\\frac{\\partial^2 \\psi}{\\partial t^2} &#8211; v^2 \\nabla^2 \\psi = 0<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Trong \u0111\u00f3:<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>\\psi l\u00e0 h\u00e0m s\u00f3ng \u0111\u1ea1i di\u1ec7n cho s\u1ef1 dao \u0111\u1ed9ng c\u1ee7a h\u1ea1t Trung,<\/li>\n\n\n\n<li>v l\u00e0 t\u1ed1c \u0111\u1ed9 truy\u1ec1n s\u00f3ng trong m\u00f4i tr\u01b0\u1eddng (v\u1eadn t\u1ed1c \u00e1nh s\u00e1ng c).<\/li>\n<\/ul>\n\n\n\n<p class=\"wp-block-paragraph\">Ph\u01b0\u01a1ng tr\u00ecnh n\u00e0y ch\u1ec9 ra r\u1eb1ng s\u1ef1 dao \u0111\u1ed9ng c\u1ee7a h\u1ea1t Trung lan truy\u1ec1n v\u1edbi v\u1eadn t\u1ed1c c\u1ed1 \u0111\u1ecbnh v = c, t\u01b0\u01a1ng t\u1ef1 nh\u01b0 s\u00f3ng \u00e2m trong kh\u00f4ng kh\u00ed nh\u01b0ng trong m\u00f4i tr\u01b0\u1eddng h\u1ea1t Trung.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><strong>3. Ph\u01b0\u01a1ng Tr\u00ecnh T\u01b0\u01a1ng T\u00e1c C\u1ee7a H\u1ea1t Trung V\u00e0 C\u00e1c H\u1ea1t Kh\u00e1c<\/strong><\/p>\n\n\n\n<p class=\"wp-block-paragraph\">M\u1eb7c d\u00f9 h\u1ea1t Trung kh\u00f4ng c\u00f3 kh\u1ed1i l\u01b0\u1ee3ng ngh\u1ec9, n\u00f3 v\u1eabn c\u00f3 th\u1ec3 t\u01b0\u01a1ng t\u00e1c v\u1edbi c\u00e1c h\u1ea1t kh\u00e1c th\u00f4ng qua c\u00e1c t\u01b0\u01a1ng t\u00e1c tr\u01b0\u1eddng. Ph\u01b0\u01a1ng tr\u00ecnh m\u00f4 t\u1ea3 s\u1ef1 t\u01b0\u01a1ng t\u00e1c c\u1ee7a h\u1ea1t Trung v\u1edbi h\u1ea1t kh\u00e1c c\u00f3 th\u1ec3 \u0111\u01b0\u1ee3c bi\u1ec3u di\u1ec5n b\u1eb1ng m\u1ed9t h\u1ec7 ph\u01b0\u01a1ng tr\u00ecnh t\u01b0\u01a1ng t\u1ef1 nh\u01b0 m\u00f4 h\u00ecnh tr\u01b0\u1eddng \u0111i\u1ec7n t\u1eeb.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">M\u1ed9t ph\u01b0\u01a1ng tr\u00ecnh c\u00f3 th\u1ec3 m\u00f4 t\u1ea3 t\u01b0\u01a1ng t\u00e1c c\u1ee7a h\u1ea1t Trung v\u1edbi m\u1ed9t h\u1ea1t c\u00f3 kh\u1ed1i l\u01b0\u1ee3ng m l\u00e0:<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">\\left( \\frac{\\partial^2}{\\partial t^2} &#8211; \\nabla^2 + \\frac{m^2}{\\hbar^2} \\right) \\psi = 0<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Trong \u0111\u00f3:<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>m l\u00e0 kh\u1ed1i l\u01b0\u1ee3ng c\u1ee7a h\u1ea1t t\u01b0\u01a1ng t\u00e1c v\u1edbi h\u1ea1t Trung,<\/li>\n\n\n\n<li>\\hbar l\u00e0 h\u1eb1ng s\u1ed1 Planck gi\u1ea3m.<\/li>\n<\/ul>\n\n\n\n<p class=\"wp-block-paragraph\">Ph\u01b0\u01a1ng tr\u00ecnh n\u00e0y ch\u1ec9 ra r\u1eb1ng s\u1ef1 t\u01b0\u01a1ng t\u00e1c gi\u1eefa h\u1ea1t Trung v\u00e0 c\u00e1c h\u1ea1t c\u00f3 kh\u1ed1i l\u01b0\u1ee3ng s\u1ebd l\u00e0m thay \u0111\u1ed5i t\u1ea7n s\u1ed1 dao \u0111\u1ed9ng c\u1ee7a h\u1ea1t Trung trong m\u00f4i tr\u01b0\u1eddng.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><strong>4. M\u00f4 H\u00ecnh N\u0103ng L\u01b0\u1ee3ng C\u1ee7a H\u1ea1t Trung<\/strong><\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Theo l\u00fd thuy\u1ebft H\u1ea1t Trung, n\u0103ng l\u01b0\u1ee3ng c\u1ee7a h\u1ea1t Trung c\u00f3 th\u1ec3 \u0111\u01b0\u1ee3c t\u00ednh b\u1eb1ng ph\u01b0\u01a1ng tr\u00ecnh n\u0103ng l\u01b0\u1ee3ng t\u1ed5ng qu\u00e1t cho c\u00e1c h\u1ea1t dao \u0111\u1ed9ng trong kh\u00f4ng gian:<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">E = \\hbar \\omega<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Trong \u0111\u00f3:<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>E l\u00e0 n\u0103ng l\u01b0\u1ee3ng c\u1ee7a h\u1ea1t Trung,<\/li>\n\n\n\n<li>\\hbar l\u00e0 h\u1eb1ng s\u1ed1 Planck gi\u1ea3m,<\/li>\n\n\n\n<li>\\omega l\u00e0 t\u1ea7n s\u1ed1 g\u00f3c c\u1ee7a dao \u0111\u1ed9ng.<\/li>\n<\/ul>\n\n\n\n<p class=\"wp-block-paragraph\">Ph\u01b0\u01a1ng tr\u00ecnh n\u00e0y ph\u1ea3n \u00e1nh m\u1ed1i quan h\u1ec7 gi\u1eefa n\u0103ng l\u01b0\u1ee3ng dao \u0111\u1ed9ng v\u00e0 t\u1ea7n s\u1ed1 dao \u0111\u1ed9ng c\u1ee7a h\u1ea1t Trung, t\u01b0\u01a1ng t\u1ef1 nh\u01b0 n\u0103ng l\u01b0\u1ee3ng c\u1ee7a photon nh\u01b0ng kh\u00f4ng y\u00eau c\u1ea7u kh\u1ed1i l\u01b0\u1ee3ng ngh\u1ec9.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><strong>5. Ph\u01b0\u01a1ng Tr\u00ecnh Schrodinger Cho H\u1ea1t Trung<\/strong><\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Trong c\u01a1 h\u1ecdc l\u01b0\u1ee3ng t\u1eed, ph\u01b0\u01a1ng tr\u00ecnh Schrodinger l\u00e0 ph\u01b0\u01a1ng tr\u00ecnh c\u01a1 b\u1ea3n m\u00f4 t\u1ea3 t\u01b0\u01a1ng t\u00e1c v\u00e0 dao \u0111\u1ed9ng c\u1ee7a c\u00e1c h\u1ea1t. \u0110\u1ed1i v\u1edbi h\u1ea1t Trung, ph\u01b0\u01a1ng tr\u00ecnh Schrodinger c\u00f3 th\u1ec3 vi\u1ebft d\u01b0\u1edbi d\u1ea1ng:<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">i \\hbar \\frac{\\partial}{\\partial t} \\psi(\\mathbf{r}, t) = &#8211; \\frac{\\hbar^2}{2m} \\nabla^2 \\psi(\\mathbf{r}, t) + V(\\mathbf{r}) \\psi(\\mathbf{r}, t)<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Trong \u0111\u00f3:<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>\\psi(\\mathbf{r}, t) l\u00e0 h\u00e0m s\u00f3ng c\u1ee7a h\u1ea1t Trung t\u1ea1i v\u1ecb tr\u00ed \\mathbf{r} v\u00e0 th\u1eddi gian t,<\/li>\n\n\n\n<li>m l\u00e0 kh\u1ed1i l\u01b0\u1ee3ng c\u1ee7a h\u1ea1t (ho\u1eb7c c\u00e1c h\u1ea1t t\u01b0\u01a1ng t\u00e1c),<\/li>\n\n\n\n<li>V(\\mathbf{r}) l\u00e0 th\u1ebf n\u0103ng t\u01b0\u01a1ng t\u00e1c c\u1ee7a h\u1ea1t Trung v\u1edbi m\u00f4i tr\u01b0\u1eddng xung quanh.<\/li>\n<\/ul>\n\n\n\n<p class=\"wp-block-paragraph\">Ph\u01b0\u01a1ng tr\u00ecnh Schrodinger cho h\u1ea1t Trung cung c\u1ea5p m\u1ed9t m\u00f4 h\u00ecnh l\u01b0\u1ee3ng t\u1eed v\u1ec1 dao \u0111\u1ed9ng v\u00e0 chuy\u1ec3n \u0111\u1ed9ng c\u1ee7a h\u1ea1t trong kh\u00f4ng gian.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><strong>6. Ph\u01b0\u01a1ng Tr\u00ecnh Einstein \u2013 H\u1ea1t Trung Trong L\u00fd Thuy\u1ebft T\u01b0\u01a1ng \u0110\u1ed1i<\/strong><\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Khi k\u1ebft h\u1ee3p thuy\u1ebft t\u01b0\u01a1ng \u0111\u1ed1i c\u1ee7a Einstein v\u1edbi m\u00f4 h\u00ecnh h\u1ea1t Trung, ta c\u00f3 th\u1ec3 s\u1eed d\u1ee5ng ph\u01b0\u01a1ng tr\u00ecnh n\u0103ng l\u01b0\u1ee3ng-momentum t\u1ed5ng qu\u00e1t \u0111\u1ec3 m\u00f4 t\u1ea3 h\u1ea1t Trung trong kh\u00f4ng-th\u1eddi gian cong. Ph\u01b0\u01a1ng tr\u00ecnh Einstein c\u00f3 d\u1ea1ng:<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">E^2 = p^2 c^2 + m^2 c^4<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Trong \u0111\u00f3:<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>E l\u00e0 n\u0103ng l\u01b0\u1ee3ng t\u1ed5ng c\u1ed9ng c\u1ee7a h\u1ea1t Trung,<\/li>\n\n\n\n<li>p l\u00e0 \u0111\u1ed9ng l\u01b0\u1ee3ng c\u1ee7a h\u1ea1t Trung,<\/li>\n\n\n\n<li>c l\u00e0 v\u1eadn t\u1ed1c \u00e1nh s\u00e1ng,<\/li>\n\n\n\n<li>m l\u00e0 kh\u1ed1i l\u01b0\u1ee3ng ngh\u1ec9 c\u1ee7a h\u1ea1t Trung.<\/li>\n<\/ul>\n\n\n\n<p class=\"wp-block-paragraph\">Ph\u01b0\u01a1ng tr\u00ecnh n\u00e0y cho th\u1ea5y s\u1ef1 t\u01b0\u01a1ng t\u00e1c n\u0103ng l\u01b0\u1ee3ng v\u00e0 \u0111\u1ed9ng l\u01b0\u1ee3ng gi\u1eefa h\u1ea1t Trung v\u00e0 c\u00e1c h\u1ea1t kh\u00e1c trong kh\u00f4ng-th\u1eddi gian, v\u00e0 gi\u00fap gi\u1ea3i th\u00edch vi\u1ec7c photon c\u00f3 n\u0103ng l\u01b0\u1ee3ng m\u00e0 kh\u00f4ng c\u1ea7n kh\u1ed1i l\u01b0\u1ee3ng ngh\u1ec9.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><strong>K\u1ebft Lu\u1eadn<\/strong><\/p>\n\n\n\n<p class=\"wp-block-paragraph\">C\u00e1c ph\u01b0\u01a1ng tr\u00ecnh li\u00ean quan \u0111\u1ebfn h\u1ea1t Trung kh\u00f4ng ch\u1ec9 ph\u1ea3n \u00e1nh c\u00e1c kh\u00e1i ni\u1ec7m c\u01a1 b\u1ea3n v\u1ec1 s\u00f3ng, dao \u0111\u1ed9ng m\u00e0 c\u00f2n m\u1edf r\u1ed9ng ra vi\u1ec7c t\u01b0\u01a1ng t\u00e1c v\u1edbi c\u00e1c h\u1ea1t kh\u00e1c, n\u0103ng l\u01b0\u1ee3ng v\u00e0 v\u1eadt l\u00fd l\u01b0\u1ee3ng t\u1eed. Nh\u1eefng ph\u01b0\u01a1ng tr\u00ecnh n\u00e0y c\u00f3 th\u1ec3 gi\u00fap ta hi\u1ec3u r\u00f5 h\u01a1n v\u1ec1 c\u01a1 ch\u1ebf truy\u1ec1n n\u0103ng l\u01b0\u1ee3ng v\u00e0 dao \u0111\u1ed9ng trong v\u0169 tr\u1ee5, v\u00e0 c\u00f3 th\u1ec3 l\u00e0 n\u1ec1n t\u1ea3ng cho nh\u1eefng l\u00fd thuy\u1ebft v\u1eadt l\u00fd m\u1edbi trong t\u01b0\u01a1ng lai.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">N\u1ebfu b\u1ea1n mu\u1ed1n kh\u00e1m ph\u00e1 s\u00e2u h\u01a1n v\u1ec1 h\u1ea1t Trung trong c\u00e1c l\u0129nh v\u1ef1c kh\u00e1c nh\u01b0 quang h\u1ecdc l\u01b0\u1ee3ng t\u1eed hay v\u1eadt l\u00fd h\u1ea1t nh\u00e2n, m\u00ecnh c\u00f3 th\u1ec3 ti\u1ebfp t\u1ee5c m\u1edf r\u1ed9ng c\u00e1c ph\u01b0\u01a1ng tr\u00ecnh n\u00e0y. B\u1ea1n c\u00f3 mu\u1ed1n t\u00ecm hi\u1ec3u th\u00eam kh\u00f4ng?<\/p>\n","protected":false},"excerpt":{"rendered":"<p>Trong l\u00fd thuy\u1ebft m\u1edbi v\u1ec1 h\u1ea1t Trung, ch\u00fang ta gi\u1ea3 \u0111\u1ecbnh r\u1eb1ng photon kh\u00f4ng ph\u1ea3i l\u00e0 c\u00e1c h\u1ea1t di chuy\u1ec3n trong kh\u00f4ng gian m\u00e0 th\u1ef1c ch\u1ea5t ch\u1ec9 l\u00e0 nh\u1eefng dao \u0111\u1ed9ng truy\u1ec1n qua m\u00f4i tr\u01b0\u1eddng n\u1ec1n (h\u1ea1t Trung). M\u00f4i tr\u01b0\u1eddng n\u00e0y kh\u00f4ng ph\u1ea3i l\u00e0 ch\u00e2n kh\u00f4ng r\u1ed7ng, m\u00e0 l\u00e0 m\u1ed9t m\u1ea1ng l\u01b0\u1edbi h\u1ea1t v\u00f4 h\u00ecnh c\u00f3 m\u1eb7t trong to\u00e0n b\u1ed9 v\u0169 tr\u1ee5. D\u01b0\u1edbi \u0111\u00e2y l\u00e0 c\u00e1c ph\u01b0\u01a1ng tr\u00ecnh quan tr\u1ecdng li\u00ean quan \u0111\u1ebfn h\u1ea1t Trung, t\u1eeb c\u00e1c m\u00f4 h\u00ecnh c\u01a1 b\u1ea3n \u0111\u1ebfn c\u00e1c ph\u01b0\u01a1ng tr\u00ecnh ph\u1ee9c t\u1ea1p h\u01a1n trong v\u1eadt l\u00fd l\u00fd thuy\u1ebft.<\/p>\n","protected":false},"author":1,"featured_media":1389,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[430],"tags":[554,553,552,556,551,555],"class_list":["post-15","post","type-post","status-publish","format-standard","has-post-thumbnail","hentry","category-vat-ly-ly-thuyet","tag-gia-dinh","tag-hat-trung","tag-ly-thuyet-moi","tag-moi-truong-nen","tag-phuong-trinh","tag-phuong-trinh-hat-trung"],"yoast_head":"<!-- This site is optimized with the Yoast SEO plugin v28.7 - https:\/\/yoast.com\/product\/yoast-seo-wordpress\/ -->\n<title>C\u00e1c Ph\u01b0\u01a1ng Tr\u00ecnh Li\u00ean Quan \u0110\u1ebfn H\u1ea1t Trung \u2013 Ph\u00e2n T\u00edch T\u1eeb C\u01a1 B\u1ea3n \u0110\u1ebfn N\u00e2ng Cao - Solio.online Blog<\/title>\n<meta name=\"robots\" content=\"index, follow, max-snippet:-1, max-image-preview:large, max-video-preview:-1\" \/>\n<link rel=\"canonical\" href=\"https:\/\/solio.online\/blog\/cac-phuong-trinh-lien-quan-den-hat-trung-phan-tich-tu-co-ban-den-nang-cao\/\" \/>\n<meta property=\"og:locale\" content=\"vi_VN\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"C\u00e1c Ph\u01b0\u01a1ng Tr\u00ecnh Li\u00ean Quan \u0110\u1ebfn H\u1ea1t Trung \u2013 Ph\u00e2n T\u00edch T\u1eeb C\u01a1 B\u1ea3n \u0110\u1ebfn N\u00e2ng Cao - Solio.online Blog\" \/>\n<meta property=\"og:description\" content=\"Trong l\u00fd thuy\u1ebft m\u1edbi v\u1ec1 h\u1ea1t Trung, ch\u00fang ta gi\u1ea3 \u0111\u1ecbnh r\u1eb1ng photon kh\u00f4ng ph\u1ea3i l\u00e0 c\u00e1c h\u1ea1t di chuy\u1ec3n trong kh\u00f4ng gian m\u00e0 th\u1ef1c ch\u1ea5t ch\u1ec9 l\u00e0 nh\u1eefng dao \u0111\u1ed9ng truy\u1ec1n qua m\u00f4i tr\u01b0\u1eddng n\u1ec1n (h\u1ea1t Trung). M\u00f4i tr\u01b0\u1eddng n\u00e0y kh\u00f4ng ph\u1ea3i l\u00e0 ch\u00e2n kh\u00f4ng r\u1ed7ng, m\u00e0 l\u00e0 m\u1ed9t m\u1ea1ng l\u01b0\u1edbi h\u1ea1t v\u00f4 h\u00ecnh c\u00f3 m\u1eb7t trong to\u00e0n b\u1ed9 v\u0169 tr\u1ee5. D\u01b0\u1edbi \u0111\u00e2y l\u00e0 c\u00e1c ph\u01b0\u01a1ng tr\u00ecnh quan tr\u1ecdng li\u00ean quan \u0111\u1ebfn h\u1ea1t Trung, t\u1eeb c\u00e1c m\u00f4 h\u00ecnh c\u01a1 b\u1ea3n \u0111\u1ebfn c\u00e1c ph\u01b0\u01a1ng tr\u00ecnh ph\u1ee9c t\u1ea1p h\u01a1n trong v\u1eadt l\u00fd l\u00fd thuy\u1ebft.\" \/>\n<meta property=\"og:url\" content=\"https:\/\/solio.online\/blog\/cac-phuong-trinh-lien-quan-den-hat-trung-phan-tich-tu-co-ban-den-nang-cao\/\" \/>\n<meta property=\"og:site_name\" content=\"Solio.online Blog\" \/>\n<meta property=\"article:published_time\" content=\"2025-08-16T03:17:51+00:00\" \/>\n<meta property=\"article:modified_time\" content=\"2025-11-22T23:08:42+00:00\" \/>\n<meta property=\"og:image\" content=\"https:\/\/blog.xelovio.com\/wp-content\/uploads\/2025\/08\/phuong-trinh-hat-Trung.webp\" \/>\n\t<meta property=\"og:image:width\" content=\"1024\" \/>\n\t<meta property=\"og:image:height\" content=\"1536\" \/>\n\t<meta property=\"og:image:type\" content=\"image\/webp\" \/>\n<meta name=\"author\" content=\"Trung Vu\" \/>\n<meta name=\"twitter:card\" content=\"summary_large_image\" \/>\n<meta name=\"twitter:label1\" content=\"\u0110\u01b0\u1ee3c vi\u1ebft b\u1edfi\" \/>\n\t<meta name=\"twitter:data1\" content=\"Trung Vu\" \/>\n\t<meta name=\"twitter:label2\" content=\"\u01af\u1edbc t\u00ednh th\u1eddi gian \u0111\u1ecdc\" \/>\n\t<meta name=\"twitter:data2\" content=\"8 ph\u00fat\" \/>\n<script type=\"application\/ld+json\" class=\"yoast-schema-graph\">{\"@context\":\"https:\\\/\\\/schema.org\",\"@graph\":[{\"@type\":\"Article\",\"@id\":\"https:\\\/\\\/solio.online\\\/blog\\\/cac-phuong-trinh-lien-quan-den-hat-trung-phan-tich-tu-co-ban-den-nang-cao\\\/#article\",\"isPartOf\":{\"@id\":\"https:\\\/\\\/solio.online\\\/blog\\\/cac-phuong-trinh-lien-quan-den-hat-trung-phan-tich-tu-co-ban-den-nang-cao\\\/\"},\"author\":{\"name\":\"Trung Vu\",\"@id\":\"https:\\\/\\\/solio.online\\\/blog\\\/#\\\/schema\\\/person\\\/287c2155cd174f2a66574cea8e892d5b\"},\"headline\":\"C\u00e1c Ph\u01b0\u01a1ng Tr\u00ecnh Li\u00ean Quan \u0110\u1ebfn H\u1ea1t Trung \u2013 Ph\u00e2n T\u00edch T\u1eeb C\u01a1 B\u1ea3n \u0110\u1ebfn N\u00e2ng Cao\",\"datePublished\":\"2025-08-16T03:17:51+00:00\",\"dateModified\":\"2025-11-22T23:08:42+00:00\",\"mainEntityOfPage\":{\"@id\":\"https:\\\/\\\/solio.online\\\/blog\\\/cac-phuong-trinh-lien-quan-den-hat-trung-phan-tich-tu-co-ban-den-nang-cao\\\/\"},\"wordCount\":1588,\"commentCount\":0,\"publisher\":{\"@id\":\"https:\\\/\\\/solio.online\\\/blog\\\/#organization\"},\"image\":{\"@id\":\"https:\\\/\\\/solio.online\\\/blog\\\/cac-phuong-trinh-lien-quan-den-hat-trung-phan-tich-tu-co-ban-den-nang-cao\\\/#primaryimage\"},\"thumbnailUrl\":\"https:\\\/\\\/solio.online\\\/blog\\\/wp-content\\\/uploads\\\/2025\\\/08\\\/phuong-trinh-hat-Trung.webp\",\"keywords\":[\"gi\u1ea3 \u0111\u1ecbnh\",\"h\u1ea1t Trung\",\"l\u00fd thuy\u1ebft m\u1edbi\",\"m\u00f4i tr\u01b0\u1eddng n\u1ec1n\",\"Ph\u01b0\u01a1ng Tr\u00ecnh\",\"Ph\u01b0\u01a1ng Tr\u00ecnh H\u1ea1t Trung\"],\"articleSection\":[\"V\u1eadt l\u00fd l\u00fd thuy\u1ebft\"],\"inLanguage\":\"vi\",\"potentialAction\":[{\"@type\":\"CommentAction\",\"name\":\"Comment\",\"target\":[\"https:\\\/\\\/solio.online\\\/blog\\\/cac-phuong-trinh-lien-quan-den-hat-trung-phan-tich-tu-co-ban-den-nang-cao\\\/#respond\"]}]},{\"@type\":\"WebPage\",\"@id\":\"https:\\\/\\\/solio.online\\\/blog\\\/cac-phuong-trinh-lien-quan-den-hat-trung-phan-tich-tu-co-ban-den-nang-cao\\\/\",\"url\":\"https:\\\/\\\/solio.online\\\/blog\\\/cac-phuong-trinh-lien-quan-den-hat-trung-phan-tich-tu-co-ban-den-nang-cao\\\/\",\"name\":\"C\u00e1c Ph\u01b0\u01a1ng Tr\u00ecnh Li\u00ean Quan \u0110\u1ebfn H\u1ea1t Trung \u2013 Ph\u00e2n T\u00edch T\u1eeb C\u01a1 B\u1ea3n \u0110\u1ebfn N\u00e2ng Cao - 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