Classical Mechanics [JEST National Eligibility Test (NET) (Research) Physics]: Questions 1 - 2 of 2

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Question 1

Classical Mechanics Small Oscillations and Normal Modes

Describe in Detail Essay▾

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

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.

Question 2

Classical Mechanics Conservation of Energy and Momentum

Describe in Detail Essay▾

Show that maximum kinetic energy transferred to a photon when hit by a photon of energy is , where mass of proton.

Explanation

According to Compton effect frequency shift is given by

On further solving,

But kinetic energy transferred to photon is

Clearly, the maximum kinetic energy of the proton corresponds to the case where the photon scatters backwards