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)
EditExplanation
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 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?
EditExplanation
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)
EditQuestion 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)
EditExplanation
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)
EditQuestion 6
Appeared in Year: 2000
Describe in Detail Subjective▾
Describe the Stern-Gerlach experiment and discuss its significance. (20 Marks)
EditExplanation
- 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) …