Quantum MechanicsVariational Method (CSIR (Council of Scientific & Industrial Research) Physical Sciences): Questions 6  10 of 11
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Question number: 6
» Quantum Mechanics » Variational Method
Appeared in Year: 2012
Question
What would be the ground state energy of the Hamiltonian – If variational principle is used to estimate it with the trial wavefunction with b, as the variational parameter?
(December)
Choices
Choice (4)  Response  

a. 
 
b. 
 
c. 
 
d. 

Question number: 7
» Quantum Mechanics » Variational Method
Appeared in Year: 2012
Question
A variational calculation is done with the normalized trial wavefunction for the one dimensional potential well , the ground state energy is estimated to be, (June)
Choices
Choice (4)  Response  

a. 
 
b. 
 
c. 
 
d. 

Question number: 8
» Quantum Mechanics » Variational Method
Question
Let and denote the normalized eigenstate corresponding to the ground and first excited state of a one dimensional harmonic oscillator. The uncertainty in the state is:
Choices
Choice (4)  Response  

a. 
 
b. 
 
c. 
 
d. 

Question number: 9
» Quantum Mechanics » Variational Method
Appeared in Year: 2011
Question
The wave function of the particle at time is given by , where and are the normalized eigen states with eigen values and respectively, . The shortest time after which will become orthogonal to is – (December)
Choices
Choice (4)  Response  

a. 
 
b. 
 
c. 
 
d. 

Question number: 10
» Quantum Mechanics » Variational Method
Appeared in Year: 2011
Question
If an electron is in the ground state of the hydrogen atom, the probability that its distance from the proton is more than one Bohr radius is approximately, (June)
Choices
Choice (4)  Response  

a.  0.68  
b.  0.91  
c.  0.48  
d.  0.28 