Classification of schrodinger equation?

[boderam]

the Schrödinger equation is sometimes called a wave equation and in my quantum mechanics text's they often show the wave equation comparing it to the Schrödinger 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.

 

[Meir Achuz]

Because of the i, the Schrödinger 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.

 

[sanjibghosh]

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

 

[boderam]

why is it necessary that the Schrödinger 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?

 

[Meir Achuz]

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.