       Re: Boundary problem with parameter using NDSolve

• To: mathgroup at smc.vnet.net
• Subject: [mg93355] Re: Boundary problem with parameter using NDSolve
• From: dh <dh at metrohm.ch>
• Date: Wed, 5 Nov 2008 04:51:25 -0500 (EST)
• References: <gemjh2\$4s0\$1@smc.vnet.net>

```
Hi Mikhail,

if you expand the wavefunction into base-functions, your problem becomes

an Eigenvalue problem and can be solved directly.

If you integrate the DE numerically you will have to search the enery

(shooting method).

hope this helps, Daniel

Mikhail Lemeshko wrote:

> Dear friends, I hope you can help me with the following problem.

>

> I try to solve the Schr=F6dinger equation for some arbitrary potential

> V(x):

>

> -f''[x] + V[x]*f[x] == ee*f[x]

>

> Considering discrete energy levels (ee<0), there are also boundary

> conditions f==f[some_very_big_x]==0, which are satisfied only at

> some values of the parameter ee. I wish to find the values of energy

> ee and the corresponding wavefunctions.

>

> Is there an easy method to do it with Mathematica? I mean, to write a

> code "here are the equations with boundary conditions, please find all

> values of ee in the interval from E1 to E2, where the boundary

> conditions are satisfied, and return me the list of them"?

>

> Or, I have to implement a cycle, which will increase the energy step-

> by-step and check whether the boundary conditions are satisfied?

>

>

> Thank you a lot in advance,

> Mikhail.

>

--

Daniel Huber

Metrohm Ltd.

Oberdorfstr. 68

CH-9100 Herisau

Tel. +41 71 353 8585, Fax +41 71 353 8907

E-Mail:<mailto:dh at metrohm.com>

Internet:<http://www.metrohm.com>

```

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