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    • https://phys.libretexts.org/Learning_Objects/A_Physics_Formulary/Physics/10%3A_Quantum_Physics
      Quantum mechanics, atomic physics, Schrödinger and Dirac equations
    • https://phys.libretexts.org/Courses/Georgia_State_University/GSU-TM-Introductory_Physics_II_(1112)/zz%3A_Back_Matter/10%3A_13.1%3A_Appendix_J-_Physics_Formulas_(Wevers)/1.10%3A_Quantum_Physics
      Quantum mechanics, atomic physics, Schrödinger and Dirac equations
    • https://phys.libretexts.org/Bookshelves/Quantum_Mechanics/Quantum_Mechanics_(Walet)/03%3A_The_Schrodinger_Equation/3.02%3A_Operators
      This appearance of operators (often denoted by hats) where we were used to see numbers is one of the key features of quantum mechanics.
    • https://phys.libretexts.org/Bookshelves/Quantum_Mechanics/Introductory_Quantum_Mechanics_(Fitzpatrick)/03%3A_Fundamentals_of_Quantum_Mechanics/3.05%3A_Operators
      Now, it follows from Equation ([e3.54]) that \[H \equiv -\frac{\hbar^{\,2}}{2\,m}\,\frac{\partial^{\,2}}{\partial x^{\,2}} + V(x).\] However, according to Schrödinger’s equation, ([e3.1]), we have \[-...Now, it follows from Equation ([e3.54]) that \[H \equiv -\frac{\hbar^{\,2}}{2\,m}\,\frac{\partial^{\,2}}{\partial x^{\,2}} + V(x).\] However, according to Schrödinger’s equation, ([e3.1]), we have \[-\frac{\hbar^{\,2}}{2\,m}\,\frac{\partial^{\,2}}{\partial x^{\,2}} + V(x) = {\rm i}\,\hbar\,\frac{\partial}{\partial t},\] so \[H \equiv {\rm i}\,\hbar\,\frac{\partial}{\partial t}.\] Thus, the time-dependent Schrödinger equation can be written \[\label{etimed} {\rm i}\,\hbar\,\frac{\partial\psi}{\p…

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