What Are the Core Equations of Quantum Mechanics Contradicting Relativity?

[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 field 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) field equations from memory.



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

 

[masudr]

Schrödinger 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

 

[dextercioby]

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

Daniel.

 

[Meir Achuz]

The key equation in NR QM is the Schrödinger equation:
$$\frac{-\hbar^2\nabla^2}{2m}\Psi+V\Psi=i\hbar\frac{\partial\Psi}<br /> {\partial t}$$.
This is based on T=p^2/2m.
The first relativistic QM wave equation was the Dirac equation:
$$[{\bf \alpha\cdot p}+\beta m]\Psi=i\hbar<br /> \frac{partial\Psi}{\partial t}.$$
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.

 

[professor]

thanks meir also, taking me a bit to piece togther the tex, i don't use it a ton but it gives me an ida of what to look for.