The allowed energies of a 3D harmonic oscillator

[kkabi_seo]

Hi!

I'm trying to calculate the allowed energies of each state for 3D harmonic oscillator.
En = (Nx+1/2)hwx + (Ny+1/2)hwy+ (Nz+1/2)hwz, Nx,Ny,Nz = 0,1,2,...

Unfortunately I didn't find this topic in my textbook.
Can somebody help me?

 

[DrClaude]

You simply need to consider the different possibilities for Nx, Ny, and Nz and calculate the corresponding energies.

 

[kkabi_seo]

You simply need to consider the different possibilities for Nx, Ny, and Nz and calculate the corresponding energies.

frankly, It is hard for me to understand.. Please explain more detaily.

 

[BvU]

Hello kkabi_seo,

I found a https://ecee.colorado.edu/~bart/book/book/chapter2/ch2_4.htm in another thread

$$E_{(n_x, n_y, n_z)} = (n_x+1/2)\hbar\omega_x + (n_y+1/2)\hbar\omega_y+ (n_z+1/2)\hbar\omega_z ,\ \ \ \text {nx,ny,nz = 0,1,2,...}$$So you fill in $\ (n_x, n_y, n_z) = (1,0,0)\$ to get $\ \ E_{(1,0,0)} \ \$ etc