Asked Sep 24, 2019

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

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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

V(x.t) = Aer)

Image Transcriptionclose

V(x.t) = Aer) Ae-at

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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