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
An operator is a mathematical rule (or procedure) that operating on one function transforms it into another function i.e. $Â\psi(x)=\phi(x),$ Every dynamical variable in Quantum mechanics is represented by an operator. Result of the operation $\hat{p_{x}}=-i\hbar\frac{\partial}{\partial x},$ $\hat{p_{y}}=-i\hbar\frac{\partial}{\partial y},$ $\hat{p_{z}}=-i\hbar\frac{\partial}{\partial z}$ $\hat{p}=-i\hbar\overrightarrow{\nabla}$ $\hat{K}$ = $\frac{\hat{p}^{2}}{2m}=-\frac{\hbar^{2}}{2m}\overrightarrow{\nabla}^{2}$Operations Symbol Taking the square root √ $\sqrt{x^{m}}=x^{m/2}$ Differentiation w.r.t. x $\frac{d}{dx}$ $\frac{d}{dx}(x^{m})=mx^{m-1}$ Position of Operator: $\hat{x},\hat{y},\hat{z}$ Momentum Operator $\hat{p}$ Potential Energy Operator $\hat{V}$ Kinetic Energy Operator (Hamiltonian Operator) $\hat{K}$ Energy Operator $(\hat{E})$ $i\hbar\frac{\partial}{\partial t}$
