app.py

import streamlit as st

# Define course outlines
phy504 = """
# PHY 504: Classical Mechanics (Advanced Mechanics)
This course focuses on a detailed and sophisticated approach to classical mechanics, emphasizing mathematical methods and applications to physical systems.

## Outline:
1. **Lagrangian Mechanics**
   - Principle of least action
   - Euler-Lagrange equations
   - Constraints and generalized coordinates
2. **Variational Principles**
   - Hamilton's principle
   - Symmetries and Noether’s theorem
3. **Hamiltonian Mechanics**
   - Hamilton’s equations of motion
   - Canonical transformations
4. **Phase Space and Liouville's Theorem**
   - Phase space flow and conservation
5. **Central Force Problems**
   - Orbital mechanics
   - Scattering in central forces
6. **Small Oscillations**
   - Normal modes
   - Perturbation methods
7. **Rigid Body Dynamics**
   - Euler angles and rotational motion
   - Inertia tensors and principal axes
   - Gyroscopic motion
8. **Nonlinear Dynamics and Chaos**
   - Bifurcation theory
   - Lyapunov exponents
   - Poincaré maps
9. **Relativistic Mechanics**
   - Lorentz transformations and four-vectors
   - Action for relativistic particles
"""

phy611 = """
# PHY 611: Quantum Mechanics I
This course provides a rigorous foundation in quantum theory, with a focus on the mathematical formalism and physical interpretation.

## Outline:
1. **Mathematical Foundations of Quantum Mechanics**
   - Hilbert spaces and operators
   - Eigenvalue problems
   - Dirac notation
2. **Postulates of Quantum Mechanics**
   - State vectors and observables
   - Measurement postulates
   - Time evolution of quantum states
3. **Harmonic Oscillator and Operator Methods**
   - Creation and annihilation operators
   - Ladder operator techniques
   - Coherent states
4. **Angular Momentum**
   - Commutation relations
   - Spin and orbital angular momentum
   - Addition of angular momenta
5. **Symmetry in Quantum Mechanics**
   - Group theory applications
   - Parity, time reversal, and charge conjugation
   - Conservation laws and symmetries
6. **Approximation Methods**
   - Time-independent perturbation theory
   - Variational methods
   - WKB approximation
7. **Quantum Systems in External Fields**
   - Magnetic fields and the Aharonov-Bohm effect
   - Stark and Zeeman effects
8. **Scattering Theory**
   - Partial wave analysis
   - Born approximation
   - Cross sections and scattering amplitudes
9. **Path Integral Formulation of Quantum Mechanics**
   - Feynman path integrals
   - Applications to quantum field theory
"""

phy613 = """
# PHY 613: Statistical Physics
This course covers the statistical description of systems with many degrees of freedom, focusing on both equilibrium and non-equilibrium phenomena.

## Outline:
1. **Review of Thermodynamics**
   - Laws of thermodynamics
   - Thermodynamic potentials
   - Phase transitions and critical phenomena
2. **Microcanonical, Canonical, and Grand Canonical Ensembles**
   - Partition functions and thermodynamic properties
   - Connections between ensembles
   - Quantum statistics: Bose-Einstein and Fermi-Dirac distributions
3. **Statistical Ensembles and Entropy**
   - Entropy as a measure of disorder
   - Gibbs entropy formula
   - Boltzmann distribution
4. **Ideal and Interacting Gases**
   - Classical ideal gas
   - Quantum ideal gases (Bose and Fermi gases)
   - Virial expansion and interactions
5. **Phase Transitions**
   - Landau theory
   - Critical exponents and universality
   - Renormalization group theory
6. **Non-equilibrium Statistical Mechanics**
   - Boltzmann equation
   - Langevin and Fokker-Planck equations
   - Brownian motion
7. **Fluctuations and Response Theory**
   - Fluctuation-dissipation theorem
   - Linear response theory
   - Kubo formalism
"""

phy614 = """
# PHY 614: Electromagnetism I (Electromagnetic Theory I)
This course covers the fundamentals of electromagnetic theory, with a deep dive into Maxwell's equations and their applications.

## Outline:
1. **Maxwell’s Equations**
   - Integral and differential forms
   - Boundary conditions
   - Continuity equation and gauge invariance
2. **Electrostatics**
   - Poisson’s and Laplace’s equations
   - Green’s functions and boundary value problems
   - Multipole expansions
3. **Magnetostatics**
   - Biot-Savart law
   - Vector potentials
   - Magnetic dipoles and multipoles
4. **Electromagnetic Waves**
   - Plane waves in vacuum and matter
   - Reflection, refraction, and polarization
   - Waveguides and cavities
5. **Radiation from Moving Charges**
   - Lienard-Wiechert potentials
   - Dipole and quadrupole radiation
   - Synchrotron and bremsstrahlung radiation
6. **Special Relativity and Electromagnetism**
   - Lorentz transformations
   - Covariant formulation of electromagnetism
   - Relativistic kinematics and dynamics
7. **Electromagnetic Field in Matter**
   - Polarization and magnetization
   - Boundary conditions at interfaces
   - Electromagnetic waves in dispersive and conducting media
"""

phy615 = """
# PHY 615: Quantum Mechanics II
This advanced course in quantum mechanics delves into more complex quantum systems, focusing on applications and advanced techniques.

## Outline:
1. **Review of Quantum Mechanics I**
   - Key principles and formalism
   - Advanced applications of harmonic oscillator
2. **Advanced Scattering Theory**
   - S-matrix and optical theorem
   - Scattering in three dimensions
   - Coulomb scattering and partial waves
3. **Relativistic Quantum Mechanics**
   - Klein-Gordon and Dirac equations
   - Spin-1/2 particles and relativistic wave equations
   - Zitterbewegung and antiparticles
4. **Quantum Field Theory Basics**
   - Quantization of fields
   - Path integrals in field theory
   - Interaction picture and perturbation theory
5. **Quantum Electrodynamics (QED)**
   - Feynman diagrams and rules
   - Renormalization and gauge symmetry
   - Applications to atomic physics
6. **Symmetry and Group Theory in Quantum Mechanics**
   - Lie groups and Lie algebras
   - Representations of symmetry groups
   - Wigner-Eckart theorem and selection rules
7. **Many-Body Quantum Mechanics**
   - Second quantization formalism
   - Hartree-Fock method
   - Bose-Einstein condensation and fermionic systems
"""

phy632 = """
# PHY 632: Advanced Topics in Theoretical Physics
This course explores contemporary and cutting-edge topics in theoretical physics, often including current research trends and advanced mathematical methods.

## Outline:
1. **Quantum Field Theory II**
   - Renormalization group theory
   - Gauge theories and spontaneous symmetry breaking
   - Anomalies and the Standard Model
2. **Supersymmetry**
   - Supersymmetric quantum mechanics
   - Superfields and superspace
   - Applications to particle physics and string theory
3. **String Theory Basics**
   - Bosonic strings and superstrings
   - D-branes and dualities
   - Holography and AdS/CFT correspondence
4. **Advanced General Relativity**
   - Gravitational waves
   - Black hole thermodynamics
   - Cosmology and inflation
5. **Topological Quantum Field Theory**
   - Chern-Simons theory
   - Topological insulators and anyons
   - Applications to condensed matter physics
6. **Nonperturbative Methods in Quantum Field Theory**
   - Instantons and solitons
   - Lattice gauge theory
   - Large N expansion and dualities
7. **Quantum Computing and Quantum Information**
   - Qubits and quantum gates
   - Quantum algorithms and complexity
   - Quantum error correction and entanglement entropy
"""

# Streamlit app to display the outlines
st.title("Graduate Physics Course Outlines")

tab1, tab2, tab3, tab4, tab5, tab6 = st.tabs(["PHY 504", "PHY 611", "PHY 613", "PHY 614", "PHY 615", "PHY 632"])

with tab1:
    st.markdown(phy504)

with tab2:
    st.markdown(phy611)

with tab3:
    st.markdown(phy613)

with tab4:
    st.markdown(phy614)

with tab5:
    st.markdown(phy615)

with tab6:
    st.markdown(phy632)