Particle in a Box: Degeneracy Explained

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Discussion Overview

The discussion centers on the concept of degeneracy in quantum mechanics, specifically regarding a particle in an infinite square well. Participants explore whether different energy eigenstates can yield the same energy value and the conditions under which degeneracy might occur.

Discussion Character

  • Conceptual clarification, Debate/contested

Main Points Raised

  • Some participants inquire whether degeneracy can occur for different energy eigenstates in the context of a particle in a box.
  • One participant questions if it is possible to obtain the same energy value with two different quantum numbers (n).
  • Another participant expresses doubt about the concept of degeneracy and suggests that it should not occur in this scenario.
  • One participant explains that degeneracy in energy typically arises when there are commuting operators with the Hamiltonian and asserts that degeneracy cannot occur in a one-dimensional system.

Areas of Agreement / Disagreement

Participants do not reach a consensus on the occurrence of degeneracy in this context, with differing viewpoints on whether it can happen in a one-dimensional infinite square well.

Contextual Notes

Some limitations include the dependence on the dimensionality of the system and the specific definitions of degeneracy being discussed. The discussion does not resolve the mathematical implications of these claims.

Joydeep Munshi
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Hi,
in case of a particle inside a box (infinite square well), can degeneracy occur for different energy eigen states?
please explain...
 
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What do you think? Can you get the same value of energy with two different values of n?
 
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Joydeep Munshi said:
Hi,
in case of a particle inside a box (infinite square well), can degeneracy occur for different energy eigen states?
please explain...
Is this homework?
 
@jtbell yes degeneracy should not occur in that case...was in doubt about the concept of degeneracy... Thanks
 
Degeneracy in energy usually arises when there are one or more operators which commute with the Hamiltonian. Moreover, in 1D system it can be shown that degeneracy cannot occur, for example see http://www.physicspages.com/2012/08/23/degenerate-solutions-dont-exist-in-one-dimension/
 
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