## Quantum Mechanics Questions and Answers in PDF

- What do you understand by matter waves? Or Discuss the concept of de-Broglie matter waves.
- Define
*group velocity and particle velocity*regarding a group wave. Or Define particle velocity, group velocity, and phase velocity. - Derive the mathematical expression for group and phase velocity.
- Show that the phase velocity of matter waves exceeds the velocity of light.
- Give the relation between group velocity and particle velocity. Or Shoe that the group velocity of matter waves equals particle velocity. Or Establish a relation between particle and group velocities.
- Show that for non-relativistic free particles the phase velocity is half of the group velocity.
- Show that group velocity is less than the phase velocity in a dispersive medium.
- Explain the Heisenberg uncertainty principle with an example. Or Prove that electrons do not exist inside the nucleus using the uncertainty principle.
- Explain the Heisenberg uncertainty principle with an example. Or Derive Heisenberg principle from the hypothetical gamma-ray microscope.
- Explain the diffraction of electrons by a single slit to illustrate the Heisenberg uncertainty principle.
- Explain the Heisenberg uncertainty principle and give an elementary proof for it.
- What do you understand by a wave function, discuss its
*physical significance*? - What is meant by operators? Get an operator for the energy “E” and momentum “P”.
- Derive
wave equation.*Schrödinger’s time-independent* - Derive Schrödinger’s time-dependent wave equation.
- Get energy level for a particle trapped in an infinitely deep square potential well.

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