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A two-dimensional harmonic oscillator can be considered as
Chapter , Problem 17P(choose chapter or problem)
Problem 17P
A two-dimensional harmonic oscillator can be considered as a system of two independent one-dimensional oscillators. Consider an isotropic two-dimensional oscillator, for which the natural frequency is the same in both directions. Write a formula for the allowed energies of this system, and draw an energy level diagram showing the degeneracy of each level.
Questions & Answers
QUESTION:
Problem 17P
A two-dimensional harmonic oscillator can be considered as a system of two independent one-dimensional oscillators. Consider an isotropic two-dimensional oscillator, for which the natural frequency is the same in both directions. Write a formula for the allowed energies of this system, and draw an energy level diagram showing the degeneracy of each level.
ANSWER:
Solution 17P
A two-dimensional harmonic oscillator can be considered as a system of two independent one-dimensional oscillators.The formula for allowed energies of this system can be written as sum of energies of two independent one dimensional harmonic oscillator.
The allowed energy for a one dimensional harmonic oscillator is
where
= 0,1,2,3.. ,
Planck’s constant ,
frequency
Step 1 of 2
The allowed energies of the system can be written as
=
+
= ()