Success Classes Technical Education - Engineering Physics - Unit Lecture

Introduction

• Lecturer: Vimal Chaudhari
• Focus: One Shoot Video for Engineering Physics, Unit 1

Objectives

• One Shoot Videos: Full unit in one video
• Content Covered: Previous year questions (PYQ), One Shoot explanations, Important questions

Preparation

• Notes: Full derivations and explanations provided
• Subscription: Subscribe to the channel and get updates on WhatsApp for PDFs and other materials
• Approach: Combination of theory + numerical examples

Unit 1 Topics

Classical Mechanics and Its Limitations

• Black Body Radiation and Ultraviolet Catastrophe: Classical physics fails to explain these phenomena
• Photoelectric Effect: Quantum mechanics explains where classical physics fails
• Double Slit Experiment: Demonstrates wave-particle duality, contradicting classical mechanics

Important Phenomena and Theories

• Plank Theory: Quantized energy levels to resolve classical inconsistencies
• De Broglie's Concept of Matter Waves: Introduction to wave-particle duality
• Schrodinger's Wave Equation: Time-independent equation for wave functions
• Physical Interpretation of Wave Function: Uses in calculating physical quantities like energy and momentum

Schrodinger Wave Equation (Time Independent)

Derivation Steps:

1. Total Energy Equation:
   • E = Kinetic Energy + Potential Energy
   • E = p²/2m + V(x)
2. Wave Function Representation:
   • ψ(x) = A e^(i(ωt - kx))
3. Differentiation:
   • First and second-order derivatives of ψ(x) with respect to x
4. Substitution:
   • Replace k with p/ħ
5. Final Form:
   • [-ħ²/2m * (d²ψ/dx²)] + V(x)ψ = Eψ, the Time-Independent Schrodinger Equation

Eigenvalues and Eigenfunctions for 1D Box

• Setup: Particle in a box with boundaries 0 and L
• Potential Function: V(x) = 0 inside the box, ∞ outside
• Wave Function Solutions: ψ(x) = A sin(kx) where k = nπ/L
• Energy Eigenvalues:
  • E_n = n² * π² * ħ² / (2mL²)
  • Quantized energy levels, n = 1, 2, 3, ...

Compton Effect and Wavelength Shift

Derivation of Wavelength Shift (Δλ)

1. Energy and Momentum Relations
2. Incorporate Photon Collisions
3. Final Equation:
   • Δλ = h/m_ec * (1 - cos θ)
4. Numerical Example Provided: Calculation of photon energy and wavelength shifts

Group Velocity vs Phase Velocity

• Phase Velocity (V_P): V_P = ω/k
• Group Velocity (V_G): V_G = dω/dk
• Relation in Non-Dispersive Medium: VG = VP
• Example and Derivation

Conclusion

• Next Steps: More One Shoot Videos upcoming for each subject
• Interaction: Comments and feedback for continuous improvement