# Classically determining velocity of particle in a box

1. Sep 22, 2011

### whatupbaby

1. The problem statement, all variables and given/known data
I am supposed to show, using a classical argument, that the speed "v" of a particle in an infinite 1-D potential well is

v= (nh)/(2mL)

2. Relevant equations

3. The attempt at a solution
Doesn't the particle just reflect back and forth against the walls of the well with a constant speed that it was given initially? How can I classically argue that planck's constant is supposed to be in the velocity?

2. Sep 22, 2011

### dynamicsolo

OK, it's "semi-classical": you use the classical concept of linear momentum ( p = mv ) , together with deBroglie's result for "particle wavelength" $\lambda = \frac{h}{p} .$

Since the potential well is "infinitely high", it has "hard walls", which we've placed at a separation L . What sort of wave will constructive interference permit in such a "box"? What are the possible wavelengths?

3. Sep 22, 2011

### whatupbaby

oh, that makes perfect sense. thanks!