# Classification of schrodinger equation?

1. Feb 25, 2009

### boderam

the schrodinger equation is sometimes called a wave equation and in my quantum mechanics text's they often show the wave equation comparing it to the schrodinger equation. i don't understand why they do this when it is of the same form as the heat equation, it's not second order in time like the wave equation. why is this? thanks in advance.

2. Feb 26, 2009

### clem

Because of the i, the Schrodinger equation does lead to traveling waves.
The exp(-t/tau) of the heat equation becomes exp(-iEt).
Because it is first order in time, a QM wave packet spreads with time.
A wave packet for the wave equation doesn't spread unless the medium is dispersive.

3. Feb 26, 2009

### sanjibghosh

Because it is first order in time, a QM wave packet spreads with time.
why so?

4. Feb 26, 2009

### boderam

why is it necessary that the schrodinger equation be first order in time? or rather, why is it necessary for the wave packet to spread in time in terms of experimental results?

Last edited: Feb 26, 2009
5. Feb 26, 2009

### clem

All QM texts show that the SE must be first order in time to preserve the norm of the the function. The spread is hard to see experimentally.
The spread is the usual spread of the diffusion equation, which is also first order in time.