Quantum Mechanics I-Particle in a Box [IAS (Admin.) Mains Physics]: Questions 1 - 6 of 10

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Question 1

Appeared in Year: 2011

Describe in Detail Subjective▾

Calculate (15 Marks)

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Explanation

… (379 more equations) …

Question 2

Appeared in Year: 2007

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In the free electron theory of metals, a conductor s regarded as consisting of free electrons in a three – dimensional box. Using the results of (a) , obtain an expression for the density of states.

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Explanation

  • Density of states, is the total number of available electronic states (or orbitals) per unit energy range at energy . To obtain the expression for , we consider the linear momentum which, in quantum mechanics, is represented by the operat…

… (765 more equations, 41 figures) …

Question 3

Appeared in Year: 2016

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Explain why the deuteron has no excited state.

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Explanation

Experimentally, there is no evidence for the existence of any excited states of the deuteron. Indeed, extending the calculations of the bound states to the cases where the orbital angular momentum quantum number is greater than zero leads to the result that the deuteron can՚t exist in these states. It will be assumed that the potential i…

… (829 more equations) …

Question 4

Appeared in Year: 2005

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The wavefunction a particle confined in a cube of volume is given by

Calculate the average values of and in the region

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Explanation

… (322 more equations) …

Question 5

Appeared in Year: 2022

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An electron in a one-dimensional infinite potential well, defined by

otherwise, goes from n = 4 to n = 2 level and emits photon of frequency Hz.

Calculate the width of the well.

(Assume Plank՚s constant J. S. and mass of electron m kg)

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Explanation

In a one-dimensional infinite potential well, the energy levels of a particle are quantized, and the allowed energy levels are given by the formula:

where: = energy of the particle in the

… (435 more equations, 5 figures) …

Question 6

Appeared in Year: 2023

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Consider a stream of a particles of mass each moving in the positive direction with kinetic energy towards the potential barrier.

for

for

Find the of particles reflected at .

(Paper 2)

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Explanation

Schrodinger equations are:

… (54 more equations) …