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Schrödinger equation for a free one dimensional particle

Schrödinger equation for a one dimensional particle with

V = 0

. The first step is to calculate the time-independent Schrödinger equation for a free one dimensional particle

Then, for each energy

E

, from the discussion at Section "Solving the Schrodinger equation with the time-independent Schrödinger equation", the solution is:

ψ (x) = \int_{E = - \infty}^{\infty} e^{\frac{2 m E i x}{ℏ}} e^{- i E t / ℏ} = e^{i \frac{2 m E x - E t}{ℏ}}

Therefore, we see that the solution is made up of infinitely many plane wave functions.

 Table of contents 150 2
- Plane wave function link Schrödinger equation for a free one dimensional particle 68
- Time-independent Schrödinger equation for a free one dimensional particle link Schrödinger equation for a free one dimensional particle 30

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