Quantum mechanics MOC

Schrödinger equation

The Schrödinger equation governs the time evolution quantum mechanical wavefunction in the Schrödinger picture. If is the state of a system at time , then

where is the Hamiltonian operator for the system. This is a linear differential system and thus solutions are given by a Quantum time evolution operator.

Time-independent Schrödinger equation

A stationary state is one for which every Observable is independent of time. They are precisely the solutions to the time-independent Schrödinger equation as obtained from Separation of variables

and are thus are energy eigenstates.¹

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Footnotes

1. 2018. Introduction to Quantum Mechanics, §2.1, pp. 27–28 ↩