Eigen value and Eigen function: Particle trapped in one-dimensional potential well

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A particle is moving in the one-dimensional box; Write and solve Schrodinger’s wave equation and get Eigenvalue and Eigen function.

Answer:

A Particle trapped in a one-dimensional potential box

(Application of time-independent Schrodinger wave equation)

If we consider a particle trapped in a one-dimensional potential box and moving along the x-axis. Let L is the width of the box and particles move between the walls of the box.

The potential energy V inside the box is 0 while on the walls and outside the wall the box potential energy V is infinite.

We defined the boundary condition as:

 

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