Classical Mechanics-Small Oscillations and Normal Modes [JEST National Eligibility Test (NET) (Research) Physics]: Questions 1 - 1 of 1

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Question 1

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Use WKB method to estimate the energy levels of a one-dimensional harmonic oscillator.

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Explanation

The classical energy of a harmonic oscillator

Now,

At turning points, and the energy is given by

On putting the value of x then,

We know Bohr-Sommerfeld quantization rule,

Here

Let,

We have,

Since,

Therefore,

Hence,

This is Harmonic Equation.