Schrodinger Equations - wave propagation

[krindik]

Hi,
Can somebody point me in the correct direction of learning about Schrödinger Equations in relation to Wave propagation. I came across Schrödinger Equations in some texts but couldn't quite understand some background. Most of the time the author used it from nowhere.

Really appreciate if you would point me to some online / book references.
Even wikipedia gives only a set of equations. I would hope some derivation/formulation based on Maxwell equations.

Thanks

 

[Peeter]

What background do you have? If you are comfortable with Fourier transforms the Dover book Quantum Theory by David Bohm does a nice job motivating this.

Note that Schrodenger's equation is not derived from Maxwell's equations.

 

[jtbell]

Perhaps this will help you:

http://hyperphysics.phy-astr.gsu.edu/hbase/quantum/schrcn.html

Click on the "balloons" to get details.

 

[krindik]

Thanks.
Yes I'm OK with Fourier transforms.
I'm looking to understand the Schrödinger relationship in the context of wave propagation.

http://hyperphysics.phy-astr.gsu.edu/hbase/quantum/schrcn.html
speaks only in abstract terms.


So far I'm happily going through understanding dispersion, dielectric loss etc. But in several references I came across the Shrodinger equation but don't know how it fits in with wave propagation.

 

[naturale]

Take the wave equation and you see that the solution can be written as
φ(x,t) = A(x) e^{- i t w} where omega is the angular frequency. De Broglie says that the energy is E = \hbar w . Now you see that the Schrödinger equation id the square root of the wave equation.

i \hbar ∂ φ(x, t) / ∂ t = E φ(x, t)

 

[sokrates]

De Broglie says that the energy is E = \hbar w

Einstein says that.

 

[naturale]

Einstein says that.

http://en.wikipedia.org/wiki/Matter_wave

maybe you are confusing with the photoelectric effect.

 

[krindik]

Thanks naturale !
That was very clear.
Anyway why is the wave equation represented as a Schrödinger equation? Is there any particular importance related to wave propagation.

I would really like to read some text with explanation like u gave + plus some insights into the importance of representing in Schrödinger equation. Could u point me to some?

Thanks

 

[naturale]

In the relativistic limit the Schrödinger equation becomes the KG equation, which (in particular in the massless case) represents a wave with velocity c. If you want to see the relation of the SE with wave equation you must study quantum field theory.

To have an idea look to http://en.wikipedia.org/wiki/Klein-Gordon_equation .

I don't how much in details you want to go, but on the interpretation of QM in terms of classical periodic waves my filling is that it is starting a new era.