Quantum Mechanics (CSIR (Council of Scientific & Industrial Research) Physical Sciences): Questions 17  20 of 80
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Question number: 17
» Quantum Mechanics » Variational Method
Appeared in Year: 2012
Question
The wave function of a state of the hydrogen atom is given by,
Where, is the normalized eigen function of the state with quantum numbers n, l and m in the usual notation. The expectation value of is the state is – (December)
Choices
Choice (4)  Response  

a. 


b. 


c. 


d. 


Question number: 18
» Quantum Mechanics » SpinStatistics Connection
Appeared in Year: 2012
Question
Consider a system of three spins S_{1}, S_{2} and S_{3} each of which can take values + 1 and –1. The energy of the system is given by , where J is a positive constant. The minimum energy and the corresponding number of spin configurations are, respectively – (December)
Choices
Choice (4)  Response  

a.  –3J and 2 

b.  – 3J and 1 

c.  J and 1 

d.  – 6J and 2 

Question number: 19
» Quantum Mechanics » Commutators and Heisenberg Uncertainty Principle
Appeared in Year: 2012
Question
The commutator is – (June)
Choices
Choice (4)  Response  

a. 


b. 


c. 


d. 


Question number: 20
» Quantum Mechanics » Timeindependent Perturbation Theory and Applications
Appeared in Year: 2013
Question
The motion of a particle of mass m in one dimension is described by the Hamiltonian. What is the difference between the (quantized) energy of the first two levels? (In the following, is the expectation value of in the ground state. )
Choices
Choice (4)  Response  

a. 


b. 


c. 


d. 

