Answer to Question #321030 in Physical Chemistry for Padma

Question

A Particle of mass m in an one dimensional potential well represented by the following:

V(x)=−W=0|x|<a|x|>a

where W is a positive constant

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1. What will be the energy of the bound state(s)?

2. Comment about the values of W and a

3. How many bound states are possible?

Answer 1

The potential energy is 0 inside the box (V=0 for 0<x<L) and goes to infinity on the walls of the box (V=∞ for x<0 or x>L). We assume that the walls have infinite potential energy to ensure that the particle has zero chance of being near the walls or outside the box. This greatly simplifies our further mathematical calculations, since we use these limiting conditions when solving the Schrеdinger equation.