CSIR Physical Sciences: Questions 177 - 179 of 401

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Question number: 177

» Quantum Mechanics » Timeindependent Perturbation Theory and Applications

Appeared in Year: 2011

MCQ▾

Question

The perturbation H=bx4 , where b is a constant, is added to the one dimensional harmonic oscillator potential V(x)=12mω2x2 . Which of the following denotes the correction to the ground state energy to first order in b?

Hint: The normalized ground state wave function of the one dimensional harmonic oscillator potential is ψ=(mωπ)14emωx22 . You may use the following integral

x2neax2dx=an12Γ(n+12)

(December)

Choices

Choice (4) Response

a.

15b24m2ω2

b.

3b24m2ω2

c.

3b22m2ω2

d.

3b22πm2ω2

Question number: 178

» Quantum Mechanics » Motion in Central Potential » Addition of Angular Momenta

Appeared in Year: 2011

MCQ▾

Question

The energy of the first excited quantum state of a particle in the two dimensional potential V(x,y)=12mω2(x2+4y2) is – (December)

Choices

Choice (4) Response

a.

3ω

b.

52ω

c.

32ω

d.

2ω

Question number: 179

» Electronics and Experimental Methods » Device Characteristics

Appeared in Year: 2011

MCQ▾

Question

A battery powers two circuits C1 and C2 as shown in the figure,

A battery powers two circuits

A Battery Powers Two Circuits

In figure a battery powers two circuits shown.

The total current I drawn from the battery is estimated by measuring the currents I1 and I2 through the individual circuits. If I1 and I2 are both 200 mA and if the errors in their measurement are 3 mA and 4 mA respectively, the error in the estimate of I is –

(December)

Choices

Choice (4) Response

a.

7.0mA

b.

5.0mA

c.

10.5mA

d.

7.5mA

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