Preparation

Prepare for Physics MSc exams

Albert Einstein

I have no special talents. I am only passionately curious.

Classical mechanics

Newton's law

Plane polar form of position, velocity and accelaration
Collision and linear momentum conservation

Non-inertial forces aka pseudo force

Fictitious forces
- Centrifugal
- Coriolis force
- Azimuthal force
Cools facts due to Coriolis force:
- Effect on weather in Earth
- Bands of Jupyter due to high angular speed than the Earth.
- Simple pendulum can't stay in a plane. It changes the plane of motion. Faucault pendulum
Science behind tides

Central force

Newton Gravitional problem(inverse square law, $V(r) = -\frac{\alpha}{r^2}$)(Klepler's problem )(Eccentricity $e = \sqrt{1+\frac{2EL^2}{m\alpha^2}}$)
Effective potential, $V_{eff}(r) = \frac{L^2}{2mr^2} + V(r)$
Three Conserved quatity
- Energy
- Angular momentum
- Runge-Lenz Vector($\vec A =$ constant vector)(for inverse square law $\vec A = \vec p \times \vec L - m \alpha \hat r$)
Cool problems in Central force field
- Captaring cross-section
- Scattering in a central force field

All about rigid body motion

Torque and angular momentum
Moment of inertia
Ellipsoid of inertia $$I = I_{xx}\cos^2\alpha + I_{yy}\cos^2\beta + I_{zz}\cos^2\gamma + 2I_{xy}\cos\alpha\cos\beta + 2 I_{yz}\cos\beta\cos\gamma + 2I_{zx}\cos\gamma\cos\alpha$$
Euler equation

$$\begin{bmatrix}\tau_1 \\ \tau_2 \\ \tau_3 \end{bmatrix} = \begin{bmatrix}I_1\dot\omega_1 + (I_3 - I_2)\omega_2 \omega_3 \\ I_2\dot\omega_2 + (I_1 - I_3)\omega_1 \omega_3 \\ I_3\dot\omega_3 + (I_2 - I_1)\omega_1 \omega_2 \end{bmatrix}$$

Free symetric top spin(Chandler Wobble of earth)

Special theory of relativity

Kinematics
Dynamics
STR and eletro-magnetism

Lagrangian and Hamiltonian mechanics

Euler Lagrange equation
- From D'Alembert's principle
- From Stationary-action principle
Legendre transformation
Hamiltonian
Advanced topics:
- Noether's theorem:For each symmetry of the Lagrangian, there is a conserved quantity.
  - Homogeneity of space $\rightarrow$ conservation of linear momentum
  - Isotropy of space $\rightarrow$ conservation of angular momentum
  - Time invarience $\rightarrow$ conservation of energy

Classical Electrodynamics

Math for Electrodynamics

Dirac Delta

Some cool problem can be dealt with Dirac delta function

Electrostatics

Coulomb's Law
Electric Field
Gauss's Law
Electric Potential
Electrostatic Boundary Conditions
Work & Energy in Electrostatics
Conductors
Laplace's Equation
Boundary Conditions & Uniqueness Theorem
The Method of Images
Multipole Expansion
Dielectrics & Polarization
Field of a Polarized Object
Gauss's Law in Presence of Dielectrics
Boundary Conditions
Linear Dielectrics
Energy in Dielectric Systems
Forces on Dielectrics

Magnetostatics

The Lorentz Force Law
The Biot-Savart Law
The Divergence and Curl of B
Magnetic Vector Potential
Magnetostatic Boundary Conditions
Multipole Expansion of The Vector Potential
Magnetization
Torques and Forces on Magnetic Dipoles
The Field of a Magnetized Object
The Auxiliary Field H
Ampere's law in Magnetized Materials * Boundary Conditions
Linear and Nonlinear Media
- Magnetic Susceptibility and Permeability
- Ferromagnetism

Electrodynamics(Electromagnetism)

Electromotive Force
- Ohm's Law
- Electromotive Force
- Motional emf
Electromagnetic Induction
- Faraday's Law
- The Induced Electric Field
- Inductance
- Energy in Magnetic Fields
Maxwell's Equations
- Electrodynamics Before Maxwell
- How Maxwell Fixed Ampere's Law
- Maxwell's Equations
- Magnetic Charge
- Maxwell's Equations in Matter
- Boundary Conditions

Electronics

Op-Amp

Analog

Solid state physics
Diode
Transistor

Digital

Sequential
- Clock
- Flipflop
- Register
Combinational

Mathematical Physics

Probability

Fourier

Differential equation

Complex analysis

Vector analysis

Linear algebra

Eigen value & Eigen vector

Optics

Wave Optics

Huygen's principle: each point of a wavefront is a source of secondary disturbance and the wavelets emanating from these points spread out in all directions with the speed of the wave. The envelope of these wavelets gives the shape of the new wavefront.

Interference
- Division of wavefront
  - Young's double slit experiment
  - Lloyd's mirror
  - Fresnel biprism
  - Fresnel two mirror
- Division of amplitude
  - Thin flim interference
  - Newton's ring
  - Michelson's interferometer
- Multiple beam interferometer
  - Febry-Perot interferometry
Diffraction
- Fraunhofer diffraction
- Fresnel diffraction
Polarization

Matrix method in optics(ray optics)

The heart:
- Translational matrix
$$\begin{bmatrix}\lambda_2 \\ y_2 \end{bmatrix} = \begin{bmatrix}1 & 0 \\ \frac{L}{n} & 1 \end{bmatrix} \begin{bmatrix}\lambda_1 \\ y_1 \end{bmatrix}$$
- Refraction matrix
$$\begin{bmatrix}\lambda_2 \\ y_2 \end{bmatrix} = \begin{bmatrix}1 & \frac{n_1 - n_2}{R} \\ 0 & 1 \end{bmatrix} \begin{bmatrix}\lambda_1 \\ y_1 \end{bmatrix}$$
Consequence from system of lens
- Unit planes and nodal plane
- Establish the lens maker formula
Thin lens
- Equivalent focus of two thin lenses

Waves

Oscilations
- Simple Pendulum
- Damped oscillator
- Forced oscillator
Wave on a string

Kinetic theory of gas and Thermodynamics

Kinetic theory of gas

Maxwell's distribution
Einstein brownian motion

Thermodynamics

Modern physics

Quantum Mechanics

QM history(Famous experiments)

Quantization of light
- Black-body radiation; Rayleigh-Jeans law
- Photoelectric effect
- Crompton effect
- Bohr model and atomic spectra

De Broglie's hypothesis brings the particle and wave theory into two sides of a same coin!

Wave charecter of electron(i.e, matter wave)
- Davisson-Germer experiment

Modern QM(i.e, from Schrödinger equation)

Hisenberg uncertainty principle
Boundary-value problems(1D problems)
- Infinite square well
- Step-potential
  - Tunneling effect

Souvik-0612 / Preparation