# Quantum Mechanics II & Atomic Physics [Optionals IAS Mains Physics]: Questions 1 - 7 of 38

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## Question 1

Appeared in Year: *2011 (IFS)*

### Describe in Detail

Essay▾Obtain the term symbols for two singlet states and two triplet states for two electron atoms. (Paper-2) (Section-A)

### Explanation

If we knowing the value of various types of angular momenta, term symbols gives three kinds of information,

Total orbital angular momentum, L

Multiplicity of the terms,

Total angular momentum,

- We can do vector sums of these vector. But it becomes easy if we consider components as these add together as scalars.
- Theref…

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## Question 2

Appeared in Year: *2011 (IFS)*

### Describe in Detail

Essay▾What are Pauli spin matrices?

Show that:

Where, are Pauli spin matrices and and are vector operators which commute with , but do not necessarily commute with each other?

### Explanation

Pauli spin matrices or Pauli matrices are a set of matrices, which are complex, Hermitian and unitary matrices. Pauli spin matrices defined as,

The Pauli vector is defined by,

From question another vector operators are and are given.

Now, mapping mechanism from a Pauli matrix basis and a vector operator basis are provided as,

Similarly,

From commutat…

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## Question 3

Appeared in Year: *2003*

### Write in Short

Short Answer▾Show that the Pauli Matrices anti commute. (5 marks)

## Question 4

Appeared in Year: *2003*

### Describe in Detail

Essay▾Express the Cartesian components of the angular momentum L in operator form. Show that . What is the significance of this commutation relation? (15 Marks)

### Explanation

The orbital angular momentum can be obtained at once by replacing by the corresponding operators in the position representation,

The Cartesian components of are

Clearly, angular momentum doesn՚t exist in a one dimensional space.

The importance of this observable is that it is compatible with any of the Cartesian components of the angular momentum

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## Question 5

Appeared in Year: *2003*

### Write in Short

Short Answer▾Show that the radial probability density of the ground state of the hydrogen atom how a maximum at . The ground state wave function of the hydrogen atom is given by Where a is the Bohr Radius (10 Marks)

## Question 6

Appeared in Year: *2000*

### Describe in Detail

Essay▾Describe the Stern-Gerlach experiment and discuss its significance. (20 Marks)

### Explanation

- Description of the experiment: First, silver (Ag) atoms are heated in an oven. The oven has a small hole through which some of the silver atoms escape. As shown in figure (1) , the beam gees through a collimator and is then subjected to an inhomogeneous magnetic field produced by a pair of pole pieces, one of which has a very sharp edge.
- We now must…

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## Question 7

### Write in Short

Short Answer▾The energy levels of a hydrogen atom are given by where Show that