Quantum Mechanics (CSIR Physical Sciences): Questions 57 - 59 of 71

Get 1 year subscription: Access detailed explanations (illustrated with images and videos) to 401 questions. Access all new questions we will add tracking exam-pattern and syllabus changes. View Sample Explanation or View Features.

Rs. 300.00 or

Question number: 57

» Quantum Mechanics » Variational Method

Appeared in Year: 2012

MCQ▾

Question

What would be the ground state energy of the Hamiltonian – H=22md2dx2αδ(x) If variational principle is used to estimate it with the trial wavefunction ψ(x)=Aebx2 with b, as the variational parameter?

(Hint:x2ne2bx2dx=(2b)n12Γ(n+12)) (December)

Choices

Choice (4) Response

a.

α2mπ2

b.

mα2π2

c.

mα222

d.

2mα2π2

Question number: 58

» Quantum Mechanics » Elementary Theory of Scattering » Born Approximation

Appeared in Year: 2012

MCQ▾

Question

A free particle describe by a plane wave and moving in the positive z – direction undergoes scattering by a potential,

V(r)={0,if x a,if x >a

If V0 is changed to 2V0 , keeping R fixed, then the differential scattering cross- section, in the Born approximation, (June)

Choices

Choice (4) Response

a.

Increases to twice the original value

b.

Decreases to one fourth the original value

c.

Increases to four times the original value

d.

Decreases to half the original value

Question number: 59

» Quantum Mechanics » Timeindependent Perturbation Theory and Applications

Appeared in Year: 2012

MCQ▾

Question

The perturbation, H={b(ax),a<x<a0,otherwise acts on a particle of mass m confined in an infinite square well potential V(x)={0,a<x<a,otherwise

The first order correction to the ground – state energy of the particle is –

(December)

Choices

Choice (4) Response

a.

ba

b.

ba2

c.

ba2

d.

2ba

f Page
Sign In