# Kinetic Energy of particle in 1D and 3D well

#### PsychonautQQ

So my professor said that the Kinetic energy of the particle in a 3D infinite well is dependent on position where in a 1D infinite well it's NOT dependent on position. She is sort of notorious for being wrong apparently and many of my undergrads are telling me she is wrong.

I understand that in a one dimensional infinite well the wavelength will be well defined so the energy will be well defined and constant everywhere, but in a 3D infinite well where the ratio of n/L for each dimension (x,y,z) are not equal to eachother, therefore the wavelength of in the x y and z direction will be different and when you combine the wavefunctions to get the surface that fits the given dimensions of the well, the wavelength won't be well defined so it seems energy of the particle won't be well defined either...

where is my thinking wrong/right??

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#### Einj

I don't know what you professor means, but the kinetic energy is usually understood as its average value over the wave function. Therefore it cannot be dependent on position since the definition of average value itself requires an integration over the coordinates of the wave function.

#### Bill_K

Science Advisor
So my professor said that the Kinetic energy of the particle in a 3D infinite well is dependent on position where in a 1D infinite well it's NOT dependent on position. She is sort of notorious for being wrong apparently and many of my undergrads are telling me she is wrong.
She is wrong.

I understand that in a one dimensional infinite well the wavelength will be well defined so the energy will be well defined and constant everywhere, but in a 3D infinite well where the ratio of n/L for each dimension (x,y,z) are not equal to eachother, therefore the wavelength of in the x y and z direction will be different and when you combine the wavefunctions to get the surface that fits the given dimensions of the well, the wavelength won't be well defined so it seems energy of the particle won't be well defined either...
The wavelengths in the x, y, z directions give the three components of the momentum, px, py, pz, The momentum p of the particle is the magnitude of the momentum vector, given by p2 = px2 + py2 + pz2, and this is independent of position.

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