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


A particle is moving in one-dimensional box; Write and solve its Schrodinger’s wave equation and obtain Eigen value 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 x-axis. Let L is the width of the box and particle move between the walls of the box.

one dimensional potential 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.

The boundary condition is defined as:

Application of time independent Schrodinger wave equation

Application of time independent Schrodinger wave equation

Application of time independent Schrodinger wave equation

Application of time independent Schrodinger wave equation

Application of time independent Schrodinger wave equation

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