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

Explain group velocity.

Set up Schrodinger equation and discuss the wavefunction.

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 calculation for an electron assuming that the uncertainty in its velocity is also 10-6 m/sec.

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 dB/dz = 3 x 105 T/m. The field gradient is perpendicular to the incident velocity of the atoms. The mass of the hydrogen atom is 1.67 x 10-27 kg. What is the separation of the two components of the beam as they emerge from the magnet?

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 and hence the quantum numbers associated with these two equations. What information can be drawn from the angular part of the Schrodinger equation? Explain.

Descrive th term 'space quantization'.

What do you mean by the wavefunction? Discuss its physical significance. Set up time-independent and time-dependent Schrodinger wave equation. What are the implications of this equation? Discuss.

Calculate uncertainty in the momentum of electron if uncertainty in its position is 1Å (10-10).

What is the probability of finding a particle in a well of width ∝ at a position α 4 from the wall if n = 1, if n = 2, if n = 3. Use the normalized wavefunction ψ(x,t) =

A small particle of mass 10-6 gm moves along the x-axis; its speed is uncertain by 10-6 m/s. (a) What is the uncertainty in the x coordinate of the particle? (b) Repeat the calculation for an electron assuming that the uncertainty in its velocity is also 10-6 m/s. Use the known values for electrons and Planck’s constant.

What is the probability of finding a particle in a well of width ∝ at a position α 4 from the wall if n = 1, if n = 2, if n = 3. Use the normalized wavefunction

Explain the theory of black body radiation .why this theory needs quantum mechanical interpretation? How this interpretation because experimentally successful ? Explain

The uncertainty in the position of a particle is equal to the de Broglie wavelength of the particle. Calculate the uncertainty in the velocity of the particle in term of the velocity of the de Broglie wave associated with the particle.