Quantum mechanics MOC

Wavefunction

In quantum mechanics, a wavefunction is a description of the quantum mechanical state of an isolated quantum system. Here is the space of all degrees of freedom. The wavefunction must satisfy Schrödinger equation, which given an initial condition describes the evolution of the wavefunction over time.

A wavefunction is said to be normalized iff for all . Since the Quantum time evolution operator is unitary, this automatically holds for all . According to Born's statistical interpretation, for a normalized wavefunction gives a probability density of observing the system in state .1 All scalar multiples of a normalized wavefunction represent the same physical state, and non-normalizable wavefunctions must be rejected as nonphysical.2

Basis

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Footnotes

  1. 2018. Introduction to Quantum Mechanics, §1.2, p. 17 ↩

  2. It begs the question, why consider non-normalized wavefunctions at all? The answer is that this is required to make the space of wavefunctions into a vector (Hilbert) space, which brings the machinery of linear algebra into the game. ↩