# JEST National Eligibility Test (NET) (Research) Physics: Questions 1 - 4 of 4

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## Question 1

### 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

### 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

## Question 3

### Describe in Detail

Essay▾**Consider the following two kets**:

**(a) Find the bra**

**(b) Evaluate the scalar product**

### Explanation

(a) We know Hermitian adjoint of kets and bras

(b) Scalar product of

## Question 4

### Describe in Detail

Essay▾**Calculate the probability that the speed of oxygen molecule lies between** **and** **at** .

### Explanation

We know probability of a molecule with speed lying between and *+* is given by

Where,

Put the values,

So, probability that the speed of oxygen molecule lies between and at 200K is .