Classically determining velocity of particle in a box

[whatupbaby]

Homework Statement

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)

Homework Equations

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?

 

[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?

 

[whatupbaby]

oh, that makes perfect sense. thanks!