(adsbygoogle = window.adsbygoogle || []).push({}); QM: Fate of a particle of an arbitrary energy in "the particle in a box" problem

1. The Doubt

Consider the situation of a particle in a box with infinite potential beyond the walls.

Ψ_{n}= √(2/L) sin(nπx/L)

E_{n}= (nπħ/L)^{2}/2m

My doubt is that what will happen, i.e. what will be the state of a single particle when left in such a box with initial kinetic energy E = ((0.2)πħ/L)^{2}/2m.

The process of leaving the particle goes as follows (in one dimension):

First an electron-gun is placed in front of a wall and then e^{-}is fired from it and suddenly after firing the e^{-}, the gun is replaced by another wall.

Note that the length of the wall is L and the gun was placed at origin.

2. The attempt at a solution

I tried to calculate it andassumedthat it's state will be:

Ψ_{n}= √(2/L) sin((0.2)πx/L)

It does obey the Schrodinger's Equation but then it doesn't obey the the boundary conditions and has a finite probability at x=L. So myassumptionwaswrong.

**Physics Forums | Science Articles, Homework Help, Discussion**

Dismiss Notice

Join Physics Forums Today!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# Homework Help: QM: Fate of a particle of an arbitrary energy in the particle in a box problem

**Physics Forums | Science Articles, Homework Help, Discussion**