Bottom ScienceQuantum Mechanics
Basic Quantum Mechanics
- 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
Advanced Quantum Mechanics
Let, $\psi(x)$ = $\hat{A}$ f(x) 1. If f(x) is real: Expectation value of momentum operator will be 0. i.e. $<\hat{p}>$ = 0 2. If the system is bound: Then also, $<\hat{p}>$ = 0 (Irrespective of the fact that f(x) is real or imaginary.) Problem: If $\psi(x)$ = 2i Sin(x), then find out expectation value for the momentum operator. Solution: Where, 2$i$ = $\hat{A}$ and f(x) = Sin(x) Here, f(x) = Sin(x) $\leftarrow$ Real Quantity So, $<\hat{p}>$ = 0Shortcut Method for Calculating Expectation Value of Momentum Operator | Quantum Mechanics
