Particle in a 2d box, using de broglie wavelength to find momentum of the particle

Consider a proton in a 2-dimensional infinite potential box with widths, L and K.

a) Using de Broglie wavelength, find the momentum of the particle.

I find some online sources that finds the energy (not momentum) using the wavefunction and seperation of variables. But the question clearly states that we should find the momentum using the de Broglie wavelength

I am a bit confused actually. How can we find the momentum just using the wavelength ?

If the box was one dimensional, the momentum could be expressed as $$p=hn/2L$$ since we have 2 dimension we will have 2 momentum component ?

Can I express my solution as $$p=p_x+p_y=hn/2K+hm/2L$$ ?

I am thinking that this is wrong. But also thinking about what question asks, I get confused

Thanks.

1 Answer

Momentum is a vector. The norm is given by $$p=\sqrt{p_x^2+p_y^2}$$.

• So I just have to take the norm of it ? And my answer is true ?? Nov 28, 2018 at 8:30