Energy levels for a 3D cubical box

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Discussion Overview

The discussion revolves around determining the energy levels for a particle in a 3D cubical box, focusing on the equations and quantum numbers involved in the calculation. The scope includes theoretical aspects and mathematical reasoning related to quantum mechanics.

Discussion Character

  • Technical explanation
  • Mathematical reasoning

Main Points Raised

  • One participant inquires about a general equation for the energy levels of a 3D cubical box.
  • Another participant provides an equation for energy levels, referencing a specific textbook, which includes terms for quantum numbers.
  • A follow-up question asks for clarification on what values to use for the quantum numbers n_x, n_y, and n_z.
  • A hint is given to consider separable sinusoidal solutions to the Schrödinger equation with appropriate boundary conditions.
  • It is noted that n_x, n_y, and n_z are quantum numbers that describe the state of the system and will appear in the energy values derived from the Schrödinger equation.

Areas of Agreement / Disagreement

The discussion does not appear to reach a consensus on the specific values or methods for determining the quantum numbers, as participants are still seeking clarification and providing hints rather than definitive answers.

Contextual Notes

Participants have not fully resolved the assumptions regarding the boundary conditions or the specific forms of the solutions to the Schrödinger equation that apply to this scenario.

cytochrome
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I'm trying to find the energies for n levels of a 3D cubical box.

Is there a general equation for this?
 
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From _Physics_, Wolfson and Pasachof, ISBN 0-673-39836-6, p. 1055:

E = h^2/8mL^2 (n^2 sub x + n^2 sub y + n^2 sub z)

CW
 
Thank you, now what do I use for the n_x, n_y, n_z?
 
Hint: try substituting separable sinusoidal solutions into the Schrödinger eqn (with suitable boundary conditions).
 
n_x , n_y , n_z are your quantum numbers, they describe your state, when you solve the Schr. Eqn. for ψ's, which are sinusoidal functions as mentioned below, n_x,y,z will appear in the energy values.
 

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