The allowed energies of a 3D harmonic oscillator

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Discussion Overview

The discussion revolves around calculating the allowed energies of a three-dimensional harmonic oscillator, focusing on the energy formula and the quantum numbers associated with each state. The scope includes theoretical aspects and mathematical reasoning related to quantum mechanics.

Discussion Character

  • Technical explanation
  • Mathematical reasoning

Main Points Raised

  • One participant presents the energy formula for a 3D harmonic oscillator: En = (Nx+1/2)hwx + (Ny+1/2)hwy + (Nz+1/2)hwz, where Nx, Ny, Nz are non-negative integers.
  • Another participant suggests considering different combinations of Nx, Ny, and Nz to calculate the corresponding energies.
  • A later reply expresses difficulty in understanding the explanation and requests a more detailed clarification.
  • One participant provides a link to additional resources and reiterates the energy formula with specific notation for the quantum numbers.

Areas of Agreement / Disagreement

Participants do not appear to reach a consensus on the clarity of the explanation, as one participant requests further detail while others provide initial guidance on the calculations.

Contextual Notes

The discussion includes varying levels of understanding among participants, with some needing more detailed explanations of the energy calculations and the application of the quantum numbers.

kkabi_seo
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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?
 
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You simply need to consider the different possibilities for Nx, Ny, and Nz and calculate the corresponding energies.
 
DrClaude said:
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.
 
Hello kkabi_seo, :welcome:

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
 

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