Bsc CSIT Semester 1 – Physics – Unit 4: Methods of Quantum Mechanics (5 Hrs.)

Question 1

Explain group velocity.

Marks: 5

Year: 2081 Final TU

1. Definition of Group Velocity Group velocity (v₍g₎) is the velocity with which a group (packet) of waves or a wave packet travels through a medium. It represents the speed of energy, information,

Question 2

Set up Schrodinger equation and discuss the wavefunction.

Marks: 5

Year: 2081 Final TU

1. Schrödinger Equation (a) Time-Dependent Schrödinger Equation The Schrödinger equation describes how the quantum state of a particle evolves with time. \[ i\hbar \frac{\partial \Psi(x,t)}{\partial

Question 3

A small particle of mass 10-6 g moves along the x axis; its speed is uncertain by 10-6 m/sec. $\quad$ (a) What is the uncertainty in the x coordinate of the particle? $\quad$ (b) Repeat the calcul

Marks: 5

Year: 2081 Final TU

Given - Uncertainty in velocity: \[ \Delta v = 10^{-6} \ \text{m s}^{-1} \] - Planck’s constant: \[ \hbar = 1.055 \times 10^{-34} \ \text{J s} \] Heisenberg Uncertainty Principle: \[ \

Question 4

A beam of hydrogen atoms is used in a Stern-Gerlach type experiment. The atoms emerge from the oven with a velocity v = 103 m/s. They enter a region 20 cm long where there is a magnetic field gradient

Marks: 5

Year: 2081 Final TU

Given Data - Velocity of hydrogen atoms, $ v = 10^{3} \, \text{m s}^{-1} $ - Length of magnetic field region, $ l = 20 \, \text{cm} = 0.20 \, \text{m} $ - Magnetic field gradient, \( \

Question 5

Setup Schrodinger equation for Hydrogen atom using spherical polar coordinates. Separate radial and angular part of this equation using appropriate separation constant. Discuss the separation constant

Marks: 10

Year: 2080 Final TU

Unit/Topic: Quantum Mechanics – Hydrogen Atom Question: Schrödinger Equation for Hydrogen Atom, Separation, and Quantum Numbers (10 Marks Answer) --- 1. Schrödinger Equation for Hydrogen Atom (2