Quantum Mechanics II & Atomic Physics [IAS (Admin.) Mains Physics]: Questions 1 - 6 of 57

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Question 1

Appeared in Year: 2011 (IFS)

Describe in Detail Subjective▾

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

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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,

Vectors Sum of Angular Momentum
  • We can do vecto…

… (344 more equations, 22 figures) …

Question 2

Appeared in Year: 2011 (IFS)

Describe in Detail Subjective▾

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?

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Explanation

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

… (424 more equations) …

Question 3

Appeared in Year: 2003

Write in Short Short Answer▾

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

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Question 4

Appeared in Year: 2003

Describe in Detail Subjective▾

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

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Explanation

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

… (354 more equations) …

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)

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Question 6

Appeared in Year: 2000

Describe in Detail Subjective▾

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

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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…

… (484 more words, 8 figures) …