# Equationins governing QM

1. Nov 30, 2005

### professor

firstly, I am deeply astounded at my typing job in the title..

what are the main equations governing qm, I am sure that atleast a few must exist, though i fail to turn them up in any place i look. To aim you more toward what i seek in particular should I be plesently surprised with a plethora of potentially intriguing equations, I wish to be pointed toward the contradictions in the equations mathmatically to those governed by relativity. Do not worry about my level of understanding in math due to my lack of knowing in the feild of qm, but i have been focusing for a long while on relativity, and by now realized that i have neglected it opposition whilst i can nearly recite the list of (Eeinstein) feild equations from memory.

-can this question be that foolish...? surely someone will comment

Last edited: Nov 30, 2005
2. Nov 30, 2005

### masudr

Schrodinger time-dependent equation which governs the time-evolution of a quantum state (or rather defines what a quantum state can be).

$$H\left|\psi\left(t\right)\right\rangle = i\hbar\frac{\partial}{\partial t}\left|\psi\left(t\right)\right\rangle$$

edit:corrected latex

Last edited: Nov 30, 2005
3. Dec 1, 2005

### dextercioby

We've also got other equations if we adopt different formulations of QM and within one formulation different pictures.

Daniel.

4. Dec 1, 2005

### Meir Achuz

The key equation in NR QM is the Schrodinger equation:
$$\frac{-\hbar^2\nabla^2}{2m}\Psi+V\Psi=i\hbar\frac{\partial\Psi} {\partial t}$$.
This is based on T=p^2/2m.
The first relativistic QM wave equation was the Dirac equation:
$$[{\bf \alpha\cdot p}+\beta m]\Psi=i\hbar \frac{partial\Psi}{\partial t}.$$
Here $$p=i\hbat\nabla.$$
The problem (gain) arose that the Dirac Eq. led to the creation of more particles and on to QFT, the only quantum theory that is compatible with SR.

Edit: correcting TEX formatting.

Last edited by a moderator: Dec 2, 2005
5. Dec 2, 2005

### professor

thanks meir also, taking me a bit to peice togther the tex, i dont use it a ton but it gives me an ida of what to look for.