- #1
yxgao
- 122
- 0
Why does the half of a harmonic oscillator potential allow only odd values of n?
Thx
Thx
Why Does a Half Harmonic Oscillator Only Allow Odd Quantum Numbers?
- Thread starter yxgao
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SUMMARY
The discussion centers on the quantum mechanics of a half harmonic oscillator potential, specifically addressing why it only permits odd quantum numbers (n). The key point is that in a half harmonic oscillator where the potential V(0) is infinite, the wave functions must satisfy the boundary condition of ψ(0) = 0. This condition inherently restricts the solutions to odd quantum numbers, as even solutions would not meet this requirement.
PREREQUISITES- Quantum Mechanics fundamentals
- Understanding of harmonic oscillator potentials
- Wave function boundary conditions
- Knowledge of quantum number quantization
- Study the mathematical formulation of harmonic oscillator wave functions
- Explore boundary conditions in quantum mechanics
- Investigate the implications of infinite potential barriers in quantum systems
- Learn about the quantization of energy levels in quantum mechanics
Students and professionals in physics, particularly those focusing on quantum mechanics, wave functions, and harmonic oscillators.
- #2
dextercioby
Science Advisor
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yxgao said:
1.What do you mean by "half of a harmonic oscillator"??You should have written the text of the problem so anyone could figure it out...
2.Today it's Christmas Day.Leave QM for tomorrow at least...
Are u going to solve QM problems on the New Year's Eve too?? Daniel.
NO QUANTUM MECHANICS ALLOWED ON CHRISTMAS!
- #3
Triss
- 80
- 0
If you mean half of a harmonic oscillator potential where [tex]V(0)=\infty[/tex], then looking at the wave functions for the full harmonic oscillator you can only admit those solutions where [tex]\psi(0)=0[/tex]. That will give you the odd solutions.
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