- #1
yxgao
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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
- Start date
In summary, a half of a harmonic oscillator potential, where the potential at the origin is infinite, only allows for odd values of n in the wave function solutions. This is due to the requirement that the wave function must be equal to zero at the origin.
- #2
- 13,349
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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... :tongue2: Are u going to solve QM problems on the New Year's Eve too?? :tongue2:
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.
What is a half harmonic oscillator?
A half harmonic oscillator is a type of system in which the restoring force is proportional to the displacement from equilibrium, but only for one half of the motion. This means that the system oscillates with a decreasing amplitude over time, rather than maintaining a constant amplitude.
What are some real-world examples of half harmonic oscillators?
Some examples of half harmonic oscillators include a pendulum with air resistance, a child on a swing, and a mass attached to a spring with a dashpot (a device that provides resistance to motion).
Can the frequency of a half harmonic oscillator be changed?
Yes, the frequency of a half harmonic oscillator can be changed by altering the characteristics of the system, such as the mass, spring constant, or damping coefficient. However, the frequency will always be proportional to the square root of the spring constant divided by the mass.
What is the difference between a half harmonic oscillator and a full harmonic oscillator?
The main difference between a half harmonic oscillator and a full harmonic oscillator is that the restoring force in a full harmonic oscillator is proportional to the displacement for the entire motion, while in a half harmonic oscillator it is only proportional for half of the motion. This results in different patterns of motion for the two systems.
How is a half harmonic oscillator used in scientific research?
Half harmonic oscillators are studied in various fields of science, including physics, engineering, and biology. They can be used to model and understand the behavior of complex systems, such as molecular vibrations, electrical circuits, and animal locomotion. Additionally, half harmonic oscillators have practical applications in fields such as seismology and earthquake engineering.
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