01: The wave function for a particle in 1-D box of length (a) is Y -Asin (7x/a). Find the value of A fora box of length 200 nm.[ Marks 5Q2: A particle of mass m moves in potential well of length 2L. Its potential energy is ( Marks 51) = (-)- {7+ > >7-and described by the wave functionV(x)*< -L and x> +L(-1) = A7+ > *> 1-*< -L and x > +LDetermine the Energy of the particle in terms of h.m and LQ3:A) The energy levels in this form E-!represents the nature of i) conductor2 m L²[Marks 3]i) semiconductor üi) insulator.B) In finite potential barrier , how far a particle penetrate in to the barrier? What is the effect of j massD energy, of the particle on penetration distance.[Marks 3]Q4: The energy of a particle in 2-D box is E- . Find the quantum numbers and the degree of2mldegeneracy.[Marks 4]05: The normalized wave function for a particle in l-D box is Y(x) - sinFind the average energy for this particle.[Marks 51

Answered: Q4: The energy of a particle in 2-D box…

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Physics

Q4: The energy of a particle in 2-D box is E- . Find the quantum numbers and the degree of 2ml degeneracy. (Marks 4)

Principles of Physics: A Calculus-Based Text

5th Edition

ISBN:9781133104261

Author:Raymond A. Serway, John W. Jewett

Publisher:Raymond A. Serway, John W. Jewett

Chapter28: Quantum Physics

Section: Chapter Questions

Problem 55P

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de Broglie Equation

The sketch of matter waves is drawn below:

Question

01: The wave function for a particle in 1-D box of length (a) is Y -Asin (7x/a). Find the value of A for
a box of length 200 nm.
[ Marks 5
Q2: A particle of mass m moves in potential well of length 2L. Its potential energy is ( Marks 51
) = (-)
- {
7+ > >7-
and described by the wave function
V(x)
*< -L and x> +L
(-1) = A
7+ > *> 1-
*< -L and x > +L
Determine the Energy of the particle in terms of h.m and L
Q3:A) The energy levels in this form E-!
represents the nature of i) conductor
2 m L²
[Marks 3]
i) semiconductor üi) insulator.
B) In finite potential barrier , how far a particle penetrate in to the barrier? What is the effect of j mass
D energy, of the particle on penetration distance.
[Marks 3]
Q4: The energy of a particle in 2-D box is E- . Find the quantum numbers and the degree of
2ml
degeneracy.
[Marks 4]
05: The normalized wave function for a particle in l-D box is Y(x) - sin
Find the average energy for this particle.
[Marks 51

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