GATE (Graduate Aptitude Test in Engineering) Physics: Questions 57  60 of 659
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Question number: 57
» Quantum Mechanics » Harmonic Oscillator
Appeared in Year: 2014
Write in Short
A one dimensional harmonic oscillator is in the superposition of number states, , given by
The average energy of the oscillator in the given state is .
Question number: 58
» Quantum Mechanics » Linear Vectors and Operators in Hilbert Space
Appeared in Year: 2015
Question
An operator for a spin particle is given by , where denotes Pauli matrices and is a constant. The eigenvalue of are –
Choices
Choice (4)  Response  

a. 


b. 


c. 


d. 


Question number: 59
» Quantum Mechanics » Postulates of Quantum Mechanics
Appeared in Year: 2015
Write in Short
Consider a system of eight non – interacting, identical quantum particle of spin in a one dimensional box of length L. The minimum excitation energy of the system, in units of is ________
Question number: 60
» Mathematical Physics » Linear Differential Equations
Appeared in Year: 2015
Question
A function satisfies the ordinary differential equation , where Consider the four statements P, Q, R, S as given below.
P: and are linearly independent solution for all values of
Q: and are linearly independent solution for all values of
R: and 1 are linearly independent solution for
S: and are linearly independent solution for all values of
The correct option for the combination of valid statements is –
Choices
Choice (4)  Response  

a.  P, R and S 

b.  Q and R 

c.  P and R 

d.  R and S 
