Useful Links
Physics
Quantum Mechanics
Core Principles and Equations
Schrödinger Equation
Time-dependent Schrödinger equation
Introduction to wave functions
Evolution of quantum states over time
Role in non-equilibrium systems
Time-independent Schrödinger equation
Stationary states and energy eigenvalues
Applications to quantum wells and oscillators
Solutions in potential wells and barriers
Applications to bound states
Quantum harmonic oscillator
Hydrogen atom
Energy quantization and spectral lines
Quantum Operators
Observables and eigenstates
Definition of observable operators
Eigenvalues as measurable quantities
Measurement postulate of quantum mechanics
Commutators
Relationship with uncertainty principle
Use in determining simultaneous observables
Calculation examples with position and momentum
Hermitian operators
Properties and significance in quantum theory
Role in ensuring real eigenvalues
Application in quantum mechanical symmetries
Bra-Ket Notation
Dirac notation
Introduction to bra and ket vectors
Simplified expression of complex quantum states
Use in quantum mechanics problems
Inner and outer products
Definition and calculation of inner products
Outer products and their use in state projections
Applications in quantum state transformations
Quantum Tunneling
Potential barrier problems
Calculation of transmission and reflection coefficients
Quantum mechanical implications of classically forbidden regions
Examples in chemical and nuclear processes
Tunneling in semiconductor devices
Role in the operation of transistors and diodes
Impact on device miniaturization
Quantum mechanical explanation of electronic conductivity
1. Fundamental Concepts
First Page
3. Interpretations of Quantum Mechanics