{"id":9173,"date":"2026-04-22T23:12:44","date_gmt":"2026-04-23T06:12:44","guid":{"rendered":"https:\/\/www.assignmenthelp.net\/blog\/?p=9173"},"modified":"2026-04-22T23:12:44","modified_gmt":"2026-04-23T06:12:44","slug":"physics-formulas-from-different-areas-of-advanced-physics","status":"publish","type":"post","link":"https:\/\/www.assignmenthelp.net\/blog\/physics-formulas-from-different-areas-of-advanced-physics\/","title":{"rendered":"Physics formulas, from different areas of advanced physics."},"content":{"rendered":"\n<p><\/p>\n\n\n<!doctype html>\n<html lang=\"en\">\n<head>\n<meta charset=\"utf-8\"\/>\n<meta content=\"width=device-width, initial-scale=1\" name=\"viewport\"\/>\n<style>         \n          table {\n              border: 1px solid #ccc; \n              border-collapse: collapse; \n              width: 100%; \n              margin: 20px 0; \n              background-color: #f9f9f9;\n          }\n          th, tr {\n            border-bottom: 1px solid #ccc; \n            background-color: #fff;\n          }\n          th, td {\n              border: 1px solid #ccc; \n              color: #333; \n              padding: 12px;\n          }       \n        <\/style>\n<\/head>\n<body>\n<p>Alright, let\u2019s go <strong>full hardcore physics mode<\/strong> \ud83d\ude04<br \/>\nHere are some <strong>seriously complex (but famous)<\/strong> physics formulas, from different areas of advanced physics.<\/p>\n<hr \/>\n<h2>\ud83d\udd2c Classical Mechanics (Advanced)<\/h2>\n<h3><strong>Euler-Lagrange Equation<\/strong><\/h3>\n<p>This one <em>runs<\/em> modern mechanics:<\/p>\n<span class=\"katex\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" display=\"block\"><semantics><mrow><mfrac><mi>d<\/mi><mrow><mi>d<\/mi><mi>t<\/mi><\/mrow><\/mfrac><\/mrow><mrow><mo fence=\"true\">(<\/mo><mfrac><mrow><mi mathvariant=\"normal\">\u2202<\/mi><mi>L<\/mi><\/mrow><mrow><mi mathvariant=\"normal\">\u2202<\/mi><msub><mover accent=\"true\"><mi>q<\/mi><mo>\u02d9<\/mo><\/mover><mi>i<\/mi><\/msub><\/mrow><\/mfrac><mo fence=\"true\">)<\/mo><\/mrow><mo>\u2212<\/mo><mfrac><mrow><mi mathvariant=\"normal\">\u2202<\/mi><mi>L<\/mi><\/mrow><mrow><mi mathvariant=\"normal\">\u2202<\/mi><msub><mi>q<\/mi><mi>i<\/mi><\/msub><\/mrow><\/mfrac><mo>=<\/mo><mn>0<\/mn><annotation encoding=\"application\/x-tex\">\\frac{d}{dt}\\left(\\frac{\\partial L}{\\partial \\dot{q}_i}\\right) &#8211; \\frac{\\partial L}{\\partial q_i} = 0<\/annotation><\/semantics><\/math><\/span>\n<p>where<\/p>\n<span class=\"katex\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" display=\"block\"><semantics><mrow><mi>L<\/mi><mo>=<\/mo><mi>T<\/mi><mo>\u2212<\/mo><mi>V<\/mi><\/mrow><annotation encoding=\"application\/x-tex\">L = T &#8211; V<\/annotation><\/semantics><\/math><\/span>\n<p>is the <strong>Lagrangian<\/strong> (kinetic energy &#8211; potential energy).<\/p>\n<hr \/>\n<h3><strong>Hamiltonian Equations<\/strong><\/h3>\n<span class=\"katex\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" display=\"block\"><semantics><mrow><msub><mover accent=\"true\"><mi>q<\/mi><mo>\u02d9<\/mo><\/mover><mi>i<\/mi><\/msub><mo>=<\/mo><mfrac><mrow><mi mathvariant=\"normal\">\u2202<\/mi><mi>H<\/mi><\/mrow><mrow><mi mathvariant=\"normal\">\u2202<\/mi><msub><mi>p<\/mi><mi>i<\/mi><\/msub><\/mrow><\/mfrac><mo separator=\"true\">,<\/mo><mspace width=\"1em\"><\/mspace><msub><mover accent=\"true\"><mi>p<\/mi><mo>\u02d9<\/mo><\/mover><mi>i<\/mi><\/msub><mo>=<\/mo><mo>\u2212<\/mo><mfrac><mrow><mi mathvariant=\"normal\">\u2202<\/mi><mi>H<\/mi><\/mrow><mrow><mi mathvariant=\"normal\">\u2202<\/mi><msub><mi>q<\/mi><mi>i<\/mi><\/msub><\/mrow><\/mfrac><\/mrow><annotation encoding=\"application\/x-tex\">\\dot{q}_i = \\frac{\\partial H}{\\partial p_i}, \\quad\n\\dot{p}_i = -\\frac{\\partial H}{\\partial q_i}<\/annotation><\/semantics><\/math><\/span>\n<p>Used in celestial mechanics, quantum mechanics, and chaos theory.<\/p>\n<hr \/>\n<h2>\u26a1 Electromagnetism (Maxwell\u2019s Equations &#8211; Full Form)<\/h2>\n<span class=\"katex\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" display=\"block\"><semantics><mrow><mi mathvariant=\"normal\">\u2207<\/mi><mo>\u22c5<\/mo><mi mathvariant=\"bold\">E<\/mi><mo>=<\/mo><mfrac><mi>\u03c1<\/mi><msub><mi>\u03b5<\/mi><mn>0<\/mn><\/msub><\/mfrac><\/mrow><annotation encoding=\"application\/x-tex\">\\nabla \\cdot \\mathbf{E} = \\frac{\\rho}{\\varepsilon_0}<\/annotation><\/semantics><\/math><\/span>\n<span class=\"katex\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" display=\"block\"><semantics><mrow><mi mathvariant=\"normal\">\u2207<\/mi><mo>\u22c5<\/mo><mi mathvariant=\"bold\">B<\/mi><mo>=<\/mo><mn>0<\/mn><\/mrow><annotation encoding=\"application\/x-tex\">\\nabla \\cdot \\mathbf{B} = 0<\/annotation><\/semantics><\/math><\/span>\n<span class=\"katex\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" display=\"block\"><semantics><mrow><mi mathvariant=\"normal\">\u2207<\/mi><mo>\u00d7<\/mo><mi mathvariant=\"bold\">E<\/mi><mo>=<\/mo><mo>\u2212<\/mo><mfrac><mrow><mi mathvariant=\"normal\">\u2202<\/mi><mi mathvariant=\"bold\">B<\/mi><\/mrow><mrow><mi mathvariant=\"normal\">\u2202<\/mi><mi>t<\/mi><\/mrow><\/mfrac><\/mrow><annotation encoding=\"application\/x-tex\">\\nabla \\times \\mathbf{E} = -\\frac{\\partial \\mathbf{B}}{\\partial t}<\/annotation><\/semantics><\/math><\/span>\n<span class=\"katex\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" display=\"block\"><semantics><mrow><mi mathvariant=\"normal\">\u2207<\/mi><mo>\u00d7<\/mo><mi mathvariant=\"bold\">B<\/mi><mo>=<\/mo><msub><mi>\u03bc<\/mi><mn>0<\/mn><\/msub><mi mathvariant=\"bold\">J<\/mi><mo>+<\/mo><msub><mi>\u03bc<\/mi><mn>0<\/mn><\/msub><msub><mi>\u03b5<\/mi><mn>0<\/mn><\/msub><mfrac><mrow><mi mathvariant=\"normal\">\u2202<\/mi><mi mathvariant=\"bold\">E<\/mi><\/mrow><mrow><mi mathvariant=\"normal\">\u2202<\/mi><mi>t<\/mi><\/mrow><\/mfrac><\/mrow><annotation encoding=\"application\/x-tex\">\\nabla \\times \\mathbf{B} = \\mu_0 \\mathbf{J} + \\mu_0 \\varepsilon_0 \\frac{\\partial \\mathbf{E}}{\\partial t}<\/annotation><\/semantics><\/math><\/span>\n<p>These four equations explain <strong>light, radio waves, electricity, and magnetism<\/strong> \ud83e\udd2f<\/p>\n<hr \/>\n<h2>\ud83c\udf21\ufe0f Thermodynamics &#x26; Statistical Physics<\/h2>\n<h3><strong>Boltzmann Entropy Formula<\/strong><\/h3>\n<p>Carved on Boltzmann\u2019s tombstone:<\/p>\n<span class=\"katex\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" display=\"block\"><semantics><mrow><mi>S<\/mi><mo>=<\/mo><msub><mi>k<\/mi><mi>B<\/mi><\/msub><mi>ln<\/mi><mo>\u2061<\/mo><mi mathvariant=\"normal\">\u03a9<\/mi><\/mrow><annotation encoding=\"application\/x-tex\">S = k_B \\ln \\Omega<\/annotation><\/semantics><\/math><\/span>\n<p>Where:<\/p>\n<ul>\n<li><span class=\"katex\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><semantics><mrow><mi>S<\/mi><\/mrow><annotation encoding=\"application\/x-tex\">S<\/annotation><\/semantics><\/math><\/span> = entropy<\/li>\n<li><span class=\"katex\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><semantics><mrow><mi mathvariant=\"normal\">\u03a9<\/mi><\/mrow><annotation encoding=\"application\/x-tex\">\\Omega<\/annotation><\/semantics><\/math><\/span> = number of microstates<\/li>\n<\/ul>\n<hr \/>\n<h3><strong>Partition Function<\/strong><\/h3>\n<p>The backbone of statistical mechanics:<\/p>\n<span class=\"katex\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" display=\"block\"><semantics><mrow><mi>Z<\/mi><mo>=<\/mo><munder><mo>\u2211<\/mo><mi>i<\/mi><\/munder><msup><mi>e<\/mi><mrow><mo>\u2212<\/mo><msub><mi>E<\/mi><mi>i<\/mi><\/msub><mi mathvariant=\"normal\">\/<\/mi><msub><mi>k<\/mi><mi>B<\/mi><\/msub><mi>T<\/mi><\/mrow><\/msup><\/mrow><annotation encoding=\"application\/x-tex\">Z = \\sum_i e^{-E_i \/ k_B T}<\/annotation><\/semantics><\/math><\/span>\n<hr \/>\n<h2>\ud83c\udf00 Quantum Mechanics (The Real Brain-Twisters)<\/h2>\n<h3><strong>Time-Dependent Schr\u00f6dinger Equation<\/strong><\/h3>\n<span class=\"katex\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" display=\"block\"><semantics><mrow><mi>i<\/mi><mi mathvariant=\"normal\">\u210f<\/mi><mfrac><mrow><mi mathvariant=\"normal\">\u2202<\/mi><mi mathvariant=\"normal\">\u03a8<\/mi><mo stretchy=\"false\">(<\/mo><mi mathvariant=\"bold\">r<\/mi><mo separator=\"true\">,<\/mo><mi>t<\/mi><mo stretchy=\"false\">)<\/mo><\/mrow><mrow><mi mathvariant=\"normal\">\u2202<\/mi><mi>t<\/mi><\/mrow><\/mfrac><mo>=<\/mo><\/mrow><mrow><mo fence=\"true\">(<\/mo><mo>\u2212<\/mo><mfrac><msup><mi mathvariant=\"normal\">\u210f<\/mi><mn>2<\/mn><\/msup><mrow><mn>2<\/mn><mi>m<\/mi><\/mrow><\/mfrac><msup><mi mathvariant=\"normal\">\u2207<\/mi><mn>2<\/mn><\/msup><mo>+<\/mo><mi>V<\/mi><mo stretchy=\"false\">(<\/mo><mi mathvariant=\"bold\">r<\/mi><mo separator=\"true\">,<\/mo><mi>t<\/mi><mo stretchy=\"false\">)<\/mo><mo fence=\"true\">)<\/mo><\/mrow><mi mathvariant=\"normal\">\u03a8<\/mi><mo stretchy=\"false\">(<\/mo><mi mathvariant=\"bold\">r<\/mi><mo separator=\"true\">,<\/mo><mi>t<\/mi><mo stretchy=\"false\">)<\/mo><annotation encoding=\"application\/x-tex\">i\\hbar \\frac{\\partial \\Psi(\\mathbf{r},t)}{\\partial t}\n=\n\\left(\n-\\frac{\\hbar^2}{2m}\\nabla^2 + V(\\mathbf{r},t)\n\\right)\\Psi(\\mathbf{r},t)<\/annotation><\/semantics><\/math><\/span>\n<p>This equation tells you <strong>everything quantum<\/strong> can tell you about a system.<\/p>\n<hr \/>\n<h3><strong>Expectation Value of an Operator<\/strong><\/h3>\n<span class=\"katex\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" display=\"block\"><semantics><mrow><mo stretchy=\"false\">\u27e8<\/mo><mi>A<\/mi><mo stretchy=\"false\">\u27e9<\/mo><mo>=<\/mo><mo>\u222b<\/mo><msup><mi mathvariant=\"normal\">\u03a8<\/mi><mo>\u2217<\/mo><\/msup><mo stretchy=\"false\">(<\/mo><mi>x<\/mi><mo stretchy=\"false\">)<\/mo><mtext>\u2009<\/mtext><mover accent=\"true\"><mi>A<\/mi><mo>^<\/mo><\/mover><mtext>\u2009<\/mtext><mi mathvariant=\"normal\">\u03a8<\/mi><mo stretchy=\"false\">(<\/mo><mi>x<\/mi><mo stretchy=\"false\">)<\/mo><mtext>\u2009<\/mtext><mi>d<\/mi><mi>x<\/mi><\/mrow><annotation encoding=\"application\/x-tex\">\\langle A \\rangle =\n\\int \\Psi^*(x)\\, \\hat{A}\\, \\Psi(x)\\, dx<\/annotation><\/semantics><\/math><\/span>\n<hr \/>\n<h2>\ud83c\udf0c Relativity (Ultra-Heavy Stuff)<\/h2>\n<h3><strong>Einstein Field Equations (General Relativity)<\/strong><\/h3>\n<span class=\"katex\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" display=\"block\"><semantics><mrow><msub><mi>G<\/mi><mrow><mi>\u03bc<\/mi><mi>\u03bd<\/mi><\/mrow><\/msub><mo>+<\/mo><mi mathvariant=\"normal\">\u039b<\/mi><msub><mi>g<\/mi><mrow><mi>\u03bc<\/mi><mi>\u03bd<\/mi><\/mrow><\/msub><mo>=<\/mo><mfrac><mrow><mn>8<\/mn><mi>\u03c0<\/mi><mi>G<\/mi><\/mrow><msup><mi>c<\/mi><mn>4<\/mn><\/msup><\/mfrac><msub><mi>T<\/mi><mrow><mi>\u03bc<\/mi><mi>\u03bd<\/mi><\/mrow><\/msub><\/mrow><annotation encoding=\"application\/x-tex\">G_{\\mu\\nu} + \\Lambda g_{\\mu\\nu}\n=\n\\frac{8\\pi G}{c^4} T_{\\mu\\nu}<\/annotation><\/semantics><\/math><\/span>\n<p>This describes <strong>gravity as curved spacetime<\/strong>.<\/p>\n<hr \/>\n<h3><strong>Energy-Momentum Relation<\/strong><\/h3>\n<span class=\"katex\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" display=\"block\"><semantics><mrow><msup><mi>E<\/mi><mn>2<\/mn><\/msup><mo>=<\/mo><msup><mi>p<\/mi><mn>2<\/mn><\/msup><msup><mi>c<\/mi><mn>2<\/mn><\/msup><mo>+<\/mo><msup><mi>m<\/mi><mn>2<\/mn><\/msup><msup><mi>c<\/mi><mn>4<\/mn><\/msup><\/mrow><annotation encoding=\"application\/x-tex\">E^2 = p^2 c^2 + m^2 c^4<\/annotation><\/semantics><\/math><\/span>\n<p>Special relativity classic.<\/p>\n<hr \/>\n<h2>\ud83d\udd25 Bonus: Chaos Theory<\/h2>\n<h3><strong>Lorenz Equations<\/strong><\/h3>\n<span class=\"katex\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" display=\"block\"><semantics><mrow><mfrac><mrow><mi>d<\/mi><mi>x<\/mi><\/mrow><mrow><mi>d<\/mi><mi>t<\/mi><\/mrow><\/mfrac><mo>=<\/mo><mi>\u03c3<\/mi><mo stretchy=\"false\">(<\/mo><mi>y<\/mi><mo>\u2212<\/mo><mi>x<\/mi><mo stretchy=\"false\">)<\/mo><\/mrow><annotation encoding=\"application\/x-tex\">\\frac{dx}{dt} = \\sigma(y &#8211; x)<\/annotation><\/semantics><\/math><\/span>\n<span class=\"katex\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" display=\"block\"><semantics><mrow><mfrac><mrow><mi>d<\/mi><mi>y<\/mi><\/mrow><mrow><mi>d<\/mi><mi>t<\/mi><\/mrow><\/mfrac><mo>=<\/mo><mi>x<\/mi><mo stretchy=\"false\">(<\/mo><mi>\u03c1<\/mi><mo>\u2212<\/mo><mi>z<\/mi><mo stretchy=\"false\">)<\/mo><mo>\u2212<\/mo><mi>y<\/mi><\/mrow><annotation encoding=\"application\/x-tex\">\\frac{dy}{dt} = x(\\rho &#8211; z) &#8211; y<\/annotation><\/semantics><\/math><\/span>\n<span class=\"katex\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" display=\"block\"><semantics><mrow><mfrac><mrow><mi>d<\/mi><mi>z<\/mi><\/mrow><mrow><mi>d<\/mi><mi>t<\/mi><\/mrow><\/mfrac><mo>=<\/mo><mi>x<\/mi><mi>y<\/mi><mo>\u2212<\/mo><mi>\u03b2<\/mi><mi>z<\/mi><\/mrow><annotation encoding=\"application\/x-tex\">\\frac{dz}{dt} = xy &#8211; \\beta z<\/annotation><\/semantics><\/math><\/span>\n<p>Tiny changes \u2192 totally different outcomes (hello, butterfly effect \ud83e\udd8b).<\/p>\n<hr \/>\n<p>If you want:<\/p>\n<ul>\n<li>\ud83d\udcc4 <strong>Download these as a DOCX<\/strong><\/li>\n<li>\ud83d\udcd8 <strong>Even more advanced formulas (QFT, string theory)<\/strong><\/li>\n<li>\ud83e\udde0 <strong>Explain any one formula step-by-step (easy or hardcore)<\/strong><\/li>\n<\/ul>\n<p>Just tell me how deep you want to go \ud83d\ude08\u269b\ufe0f<\/p>\n<\/body>\n<\/html>\n","protected":false},"excerpt":{"rendered":"<p>Alright, let\u2019s go full hardcore physics mode \ud83d\ude04 Here are some seriously complex (but famous) physics formulas, from different areas of advanced physics. \ud83d\udd2c Classical Mechanics (Advanced) Euler-Lagrange Equation This [&hellip;]<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[26],"tags":[1789,1790],"class_list":["post-9173","post","type-post","status-publish","format-standard","hentry","category-assignment-help","tag-assignment-help","tag-writing-help","has_no_thumb"],"_links":{"self":[{"href":"https:\/\/www.assignmenthelp.net\/blog\/wp-json\/wp\/v2\/posts\/9173","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/www.assignmenthelp.net\/blog\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/www.assignmenthelp.net\/blog\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/www.assignmenthelp.net\/blog\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/www.assignmenthelp.net\/blog\/wp-json\/wp\/v2\/comments?post=9173"}],"version-history":[{"count":1,"href":"https:\/\/www.assignmenthelp.net\/blog\/wp-json\/wp\/v2\/posts\/9173\/revisions"}],"predecessor-version":[{"id":9174,"href":"https:\/\/www.assignmenthelp.net\/blog\/wp-json\/wp\/v2\/posts\/9173\/revisions\/9174"}],"wp:attachment":[{"href":"https:\/\/www.assignmenthelp.net\/blog\/wp-json\/wp\/v2\/media?parent=9173"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.assignmenthelp.net\/blog\/wp-json\/wp\/v2\/categories?post=9173"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.assignmenthelp.net\/blog\/wp-json\/wp\/v2\/tags?post=9173"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}