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*From*: Bob Sciamanda <trebor@VELOCITY.NET>*Date*: Sun, 22 Feb 2004 22:45:24 -0500

RESUBMITTED (Things are getting lost):

Some addendum thoughts:

http://www.kw.igs.net/~jackord/bp/i4.html shows how the Schrodinger eq

emerges from

Einstein: E=hf; DeBroglie: p=h/lamda; and p^2/2m + U(x) = E.

But

1)Why did S use a first order time derivative and not a 2nd order time

derivative, as in the "standard" wave equation: (d/dx)^2 PHI(x,t) =

Const*(d/dt)^2 PHI(x,t)? and

2) Why is the imaginary (i) necessary?

1) The wave function PHI(x,t) is to be a complete description of the

particle's state at any time t. This means that the governing differential

equation must be able to develop PHI(x,t) solely from a knowledge of

PHI(x,0), where t=0 is any convenient "starting" time. This requires the

governing differential (Wave) equation to be first order in time

derivatives. A second order time derivative in the wave equation would

require a knowledge of both PHI(x,0) and (d/dt) PHI(x,0) as initial

conditions. PHI(x,0) would not alone be a complete state description.

(In the same way, the second order N2: F=m*(d/dt)^2 x(t) requires a

knowledge of both the position x and the velocity dx/dt as initial

conditions to specify and develop a particle state - given the environment,

F)

2) Now SIN[k(x-ut)] is not a solution of the first (time) order wave

equation: (d/dx)^2 PHI(x,t) = Const* d/dt PHI(x,t) :

Sines and Cosines repeat only after 2 differentiations. But the exponential

combination wave of real cosine and imaginary sine

exp[ik(x-ut)] IS a solution if we choose an imaginary Const in the wave

equation. (We speak here of a free particle.)

Bob Sciamanda

Physics, Edinboro Univ of PA (Em)

http://www.velocity.net/~trebor

trebor@velocity.net

----- Original Message -----

From: "Bob Sciamanda" <trebor@VELOCITY.NET>

To: <PHYS-L@lists.nau.edu>

Sent: Friday, February 20, 2004 3:22 PM

Subject: Re: Schrodinger equation origins

Perhapsis

http://www.kw.igs.net/~jackord/bp/i4.html

will help.

Bob Sciamanda

Physics, Edinboro Univ of PA (Em)

http://www.velocity.net/~trebor/

trebor@velocity.net

----- Original Message -----

From: "Larry Smith" <larry.smith@SNOW.EDU>

To: <PHYS-L@lists.nau.edu>

Sent: Thursday, February 19, 2004 7:34 PM

Subject: Schrodinger equation origins

One of my intro Modern Physics texts says regarding the genesis (origin)of

the Schrodinger wave equation "Like the classical wave equation, the

Schrodinger equation relates the time and space derivatives of the wave

function. Schrodinger's reasoning is somewhat difficult to follow and

not important for our purposes. In any case, the Schrodinger equation

cannot be derived, just as Newton's laws of motion cannot be derived."

Can the list give me a sense of Schrodinger's line of reasoning in

developing his wave equation?

Thanks,

Larry

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