---
tags:
  - quantum
---
$$\psi(r,\theta,\phi)=R(r)\cdot Y_{ml}(\theta, \phi)$$
Wave functions are products of
Radial Function
- $R_{n,l}(r)$
Spherical Harmonic
- $Y_{ml}(\theta, \phi)$

Forms [Orbitals](Orbitals.md)

Absolute value of wave function squared gives probability density of finding electron inside differential volume $dV$ centred on $r, \theta, \phi$

$$|\psi(r,\theta,\phi)|^2$$
![wave-function-polar](../img/wave-function-polar.png)

![hydrogen-wave-function](../img/hydrogen-wave-function.png)
![wave-function-polar-segment](../img/wave-function-polar-segment.png)
![wave-function-nodes](../img/wave-function-nodes.png)

![hydrogen-electron-density](../img/hydrogen-electron-density.png)

![radius-electron-density-wf](../img/radius-electron-density-wf.png)