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Re: Transfer matrix method

cross-posting to sci.engr.mech

> Not sure if this is the best n.g for this question > > I've got a funny-shaped potential barrier, and need to use matrix > transfer method (WKB no use here, need to see any resonance) > > I can follow the theory O.K, but tending to get stuck on > idiot stuff, like what do I choose for A,B C,D constants > in wave equations. > Anyone reccomend an idiots guide? Or a more suitable n.g? > > Steve Ralph > >
Reply to
N:dlzc D:aol T:com (dlzc)
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"N:dlzc D:aol T:com (dlzc)" wrote in message news:itvbd.898$SW3.490@fed1read01...

Yes, the ends have to join up, no problems there-

I have equations of the type

phi1(x) = Ae^ik1x + Be^-ik1x (x

Reply to
Steve Ralph

The 'open ended' ranges are one key here: To be integrable, the functions cannot grow without limit as one moves out into the open range. This constrains both B and E to identically zero.

Another 'trick' is node counting: a node is a point where the wave function vanishes. If C and D are of the same sign, there can be no node in the interval 0

Reply to
tadchem

Speaking of nodes, the document I'm working from is

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is about the only description of the basic method I've managed to find so far. I've realised WKB looses resonances, which is no good - I'm very much in instant cookbook mode at the moment :>)) I think it's finally clicked that I have expressions for d12 p2 etc in (17) so the top row of that 2x2 matrix multiplication gives t11. I'm starting to get my head round whats happening here, so thanks for some most useful comments! Doutless I'll be back in a day or so when I end up with infinite tunnelling or something equally silly

SR

Reply to
Steve Ralph

Thanx again. I graduated in physics in '76, and then got my doc in turbulent combustion flow measurement. I had to struggle to get an equation in there at all :>)) It is something of a shock to find myself with my trusty PC doing QM! It is like banging the rust off pipes. All of a sudden the math sort of came into focus, (comments from Tadchem and N:dlx wotsit helped ) so feeling a lot more competent (until the next obstacle) its down to ordinary programming and countering my tendancy to make dumb mistakes now. I just hope I can put E = Vmax and get 1, and E=Vmax=0 and get 0. (fat chance :>))

This is real fun. As an experimentalist I never expected to get involved in theoretical work, let alone get to see new territory. (Provided I can get my arithmetic right of course LOL)

Steve Ralph

Reply to
Steve Ralph

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