# Quantum Mechanics I-Particle in a Box [Optionals IAS Mains Physics]: Questions 1 - 4 of 4

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## Question 1

Appeared in Year: *2011*

### Describe in Detail

Essay▾Calculate (15 Marks)

### Explanation

For the previous problem, let as find

where As the given wave function is normalized

## Question 2

Appeared in Year: *2007*

### Describe in Detail

Essay▾In the free electron theory of metals, a conductor s regarded as consisting of free electrons in a three – dimensional box. Using the results of (a) , obtain an expression for the density of states.

### Explanation

- Density of states, is the total number of available electronic states (or orbitals) per unit energy range at energy . To obtain the expression for , we consider the linear momentum which, in quantum mechanics, is represented by the operator

- This equation represents a standing wave solution. it is however more convenient to work with the plane trav…

… (369 more words) …

## Question 3

### Explanation

Experimentally, there is no evidence for the existence of any excited states of the deuteron. Indeed, extending the calculations of the bound states to the cases where the orbital angular momentum quantum number is greater than zero leads to the result that the deuteron can՚t exist in these states. It will be assumed that the potential is central …

… (254 more words) …

## Question 4

Appeared in Year: *2005*

### Describe in Detail

Essay▾The wavefunction a particle confined in a cube of volume is given by

Calculate the average values of and in the region

### Explanation

Solving only x part as of now:

Because x lies between

First let us solve only integral:

=

Denominator

As

(As the wavefunction is normalized)