Quantum Physics Lecture Notes

Introduction

Instructor: Sanju Badhe, K.J. Somaya Institute of Engineering and Information Technology
Topics Covered:
- De Broglie hypothesis of matter waves
- Heisenberg uncertainty principle
- Schrodinger's equations
Structure of the Lecture Series:
- Introduction to matter waves
- Properties of matter waves
- Wave packet concepts
- Heisenberg uncertainty principle
- Schrodinger's equations (time-dependent and time-independent)
- Applications of quantum physics (quantum coding)

Concept: First introduced by Max Planck to explain black body radiation.
- Black Body: Absorbs 99.9% of incident radiation; designed as a hollow sphere with a narrow hole coated in carbon black.
Radiation Emission: After absorbing radiation, it emits radiation through the hole characterized by all wavelengths.
Intensity vs. Wavelength Curve:
- Higher wavelengths have low intensity; shorter wavelengths have more intensity.
- Peak wavelength (λ_max) is where intensity is maximum.
Temperature Dependency:
- As temperature increases, λ_max shifts left (toward shorter wavelengths). Explained by Wien’s Displacement Law:
  - λ_max is inversely proportional to temperature.
Limitations of Previous Laws:
- Wien's Law: only explains shorter wavelengths.
- Rayleigh-Jeans Law: explains longer wavelengths but fails at shorter wavelengths.

Planck's Proposal: Radiated energy depends on frequency, formulated as E = hν (where h is Planck's constant).
Average Energy Calculation:
- Average energy using Boltzmann distribution:
  [ E_{avg} = \frac{hν}{e^{\frac{hν}{kT}} - 1} ]
- Resulting Planck's radiation law: [ \rho v = \frac{8πhν^3}{c^3} \cdot \frac{1}{e^{\frac{hν}{kT}} - 1} ]_

Einstein's Contribution: Used Planck's theory to explain the photoelectric effect, confirming light's dual nature as both particle and wave.
Macroscopic vs. Microscopic: Classical mechanics applies to larger particles; quantum mechanics needed for microscopic particles.

Main Assertion: "There is a wave associated with every moving particle."
- Wavelength equation: [ λ = \frac{h}{p} ] (where p = momentum = mv).
Justification:
- Supported by Planck's and Einstein's theories.
- Relates to Bohr's postulates about quantized angular momentum in electrons.

Setup: Electron gun with tungsten filament; electrons produced via thermionic emission.
Diffraction Grating: Nickel crystal acts as a grating for electrons.
Findings:
- Diffraction pattern confirmed existence of wave associated with electrons.
- Two peaks in the intensity graph indicated wave behavior.
Calculations:
- Wavelength calculated using de Broglie relation and compared to Bragg's Law.
- Results from both methods matched, confirming de Broglie hypothesis validity.

Key Takeaways:
- De Broglie hypothesis successfully introduces wave-particle duality for all matter, not just photons.
- Experimental verification supports both parts of the hypothesis.
Next Sessions: Numerical problems on de Broglie hypothesis, Heisenberg uncertainty principle, and Schrodinger equations.

Planck awarded Nobel Prize in 1918 for his contributions.
Matter waves are not electromagnetic; they can propagate in a vacuum and are associated with all types of particles.
Phase velocity of matter waves can exceed the speed of light.