Bottom Science- Origin of Quantum Physics
- Wave function
- Collapse of Wave Function
- Physically Accepted Wave function
- Normalization Explained
- Method of Normalization
- Orthogonality & Orthonormality
- Hilbert Space
- Quantization Rules
- Operator Formalism
- Commutator Bracket
- Linear Operator
- Hermitian Operator
- Projection Operator
- Unitary Operator
- Parity Operator
- Expectation Value
- Schrodinger Equation
- Wave-Particle Duality Using Schrodinger Equation
- Superposition of States
- Various Representations of Wave Function
- Probability Current Density
- Uncertainty in Operators
- Shortcut for Calculating Momentum Expectation Value
if $|\phi_{1}\succ,|\phi_{2}\succ,|\phi_{3}\succ……|\phi_{n}\succ$ are orthonormal state vectors/wave functions and are represnting state of quantum mechanics system. Then any linear combination will also represent the state of a quantum mechanics system. In other words, if $\phi_{1},\phi_{2},…..\phi_{n}$ are solutions of Schrodinger equation, then linear combination/superposition of the states i.e. $|\psi\succ=C_{1}|\phi_{1}\succ+C_{2}|\phi_{2}\succ+C_{3}|\phi_{3}\succ+…….$ $=\sum_{n}C_{n}|\phi_{n}\succ$ will also be a solution of Schrodinger equation. Note: (1) $|\psi\succ$ will be normalized if: $|C_{1}|^{2}+|C_{2}|^{2}+|C_{3}|^{2}=1$ (2) Probability of finding a particle in $|\phi_{1}\succ state: =|C_{1}|^{2}=|\prec\phi_{1}|\psi\succ|^{2}$
