andy
d7ab8f329a
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1.2 KiB
1.2 KiB
-\frac{\hbar^2}{2m}\nabla^2\psi+V\psi=E\psi
- Time Independent
\psi
is the Wave Function
Quantum counterpart of Newton's second law in classical mechanics
F=ma
Given a set of known initial conditions, Newton's second law makes a mathematical prediction as to what path a given physical system will take over time. The Schrödinger equation gives the evolution over time of a wave function, the quantum-mechanical characterization of an isolated physical system.
Time–Independent Schrödinger Equation RadialEquation.pdf
Hamiltonian
-
Operator
-
Total energy of a system
-
Kinetic + Potential energy
\hat{H}=\hat{T}+\hat{V}
\hat{V}
- Potential Energy
\hat{T}=\frac{\hat{p}\cdot\hat{p}}{2m}=-\frac{\hbar^2}{2m}\nabla^2
- Kinetic Energy
\hat{p}=-i\hbar\nabla
- Momentum operator
Wavefunction Normalisation
- Adds up to 1 under the curve