Question

Asked Sep 24, 2019

How do you use the Schrodinger equation to determine a particle’s position in free space?

Step 1

The one Dimensional Time dependent Schrodinger wave equation for a particle in a potential *V(x,t)* is expressed as

Step 2

Here, *ψ(x,t)* represents the wave function of the particle in one dimension, *V(x,t) *represents the potential function of the particle,* m *is the mass of the particle

For a free particle in one dimension,

*V(x,t)* = 0.

Solution for this equation will be in the form of a complex plane wave specified by

Step 3

Here, *A* is the amplitude of the complex plane wave, *k *is the wave vector of the free particle, and *ω* is the angular frequency of the propagating free particle.

Since the wave function for *ψ(x ,t) *represents a plane wave.

The plane wave solution of ...

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