Quantum Mechanics (CSIR Physical Sciences): Questions 66 - 68 of 70

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Question number: 66

» Quantum Mechanics » Timeindependent Perturbation Theory and Applications

Appeared in Year: 2012

MCQ▾

Question

Consider an electron in a box of length L with periodic boundary condition ψ(x)=ψ(x+L) . If the electron is in the ψk(x)=1Leikx with energy εk=2k22m , what is the correction to its energy, to second order of perturbation theory, when it is subjected to weak periodic potential V(x)=V0cosgx , where g is an integral multiple of the 2πL ? (June)

Choices

Choice (4) Response

a.

V02(εkεg)εg2

b.

V02εk+εg

c.

mV0222(1g2+2kg+1g22kg)

d.

V02εgεk2

Question number: 67

» Quantum Mechanics » Variational Method

Appeared in Year: 2011

MCQ▾

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.

0.48

b.

0.68

c.

0.28

d.

0.91

Question number: 68

» Quantum Mechanics » Motion in Central Potential » Hydrogen Atom

Appeared in Year: 2011

MCQ▾

Question

A particle in one dimension moves under the influence of a potential V(x)=ax6 , where a is a real constant. For large n the quantized energy level En depends on n as: (June)

Choices

Choice (4) Response

a.

En~n3

b.

En~n43

c.

En~n32

d.

En~n65

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