Particle in a Box: Degeneracy Explained

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SUMMARY

In the context of quantum mechanics, degeneracy does not occur for a particle in a one-dimensional infinite square well. Energy eigenstates are uniquely defined by their quantum number n, meaning that each value of n corresponds to a distinct energy level. The discussion clarifies that degeneracy typically arises in systems with multiple commuting operators with the Hamiltonian, which is not applicable in one-dimensional systems. For further understanding, the provided link to Physics Pages offers additional insights into the absence of degenerate solutions in one dimension.

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  • Understanding of quantum mechanics principles
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  • Basic grasp of one-dimensional infinite square well models
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Students and professionals in physics, particularly those focused on quantum mechanics, as well as educators seeking to clarify concepts related to energy eigenstates and degeneracy in quantum systems.

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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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Thread 'Two equivalent statements of time reversal symmetric Hamiltonian'

Time reversal invariant Hamiltonians must satisfy ##[H,\Theta]=0## where ##\Theta## is time reversal operator. However, in some texts (for example see Many-body Quantum Theory in Condensed Matter Physics an introduction, HENRIK BRUUS and KARSTEN FLENSBERG, Corrected version: 14 January 2016, section 7.1.4) the time reversal invariant condition is introduced as ##H=H^*##. How these two conditions are identical?
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