I tried to work out the transmission coefficient and(adsbygoogle = window.adsbygoogle || []).push({});

the reflection coefficient for a case similar to the

one refered by this website:

http://www.chembio.uoguelph.ca/educmat/chm386/rudiment/models/barrier/barsola.htm [Broken]

but instead this time, I reverse the situation and

now, that particle I is heading from the right, ie

from a higher potential and a possibility that it will

be transmitted to the left, ie to a lower potential,

still with the same E > V.

I've drawn a diagram of the situation which I am

considering in my question using my own notations.

(As this is a bmp file, it may take some time to

load.)

http://www.geocities.com/ace_on_mark9909/reflection.htm

My confusion is regarding to the reflection and its

coefficient, which I've worked in steps here:

I state here the situation I am refering to: Supposing

the particle initially is at the potential V = 0,

heading to the left. At x = 0, there is the sudden

change in the potential to V = -V'.

Using p as the wave number, ie (2pi/lambda) for the

particle when at V = 0, and q as wave number for

particle at V = -V', I obtained the transmission

coefficient, T as 4pq/(p+q)^2.

By the condition of the potential 0 > -V', thus, p <

q, ie the wavelength at V = 0 > wavelength at V = -V'.

Let, q = ap, ie a = ratio of final wavenumber to

initial wave number: q/p. Since, q > p => a > 1.

We simplify the transmission coefficient to from

T = 4pq/(p+q)^2

to

T = 4a/(1+a)^2 ... (1)

From equation 1, it states that T is only dependent on

the ratio of the two wave number and hence dependent

only on the ratio of both wavelengths, and not on any

of the wavelength alone

=> the coefficient T does not discriminate on the size

on any of the wavelength alone but the ratio of the

magnitude of its wavelengths.

=> T does not distinguish between a particle or a

macroscopic object, eg, a ball.

From T = 4a/(1+a)^2, I've drawn a graph of it for a in

the range 0 <= a <= +infinity. I've uploaded to this

website:

http://www.geocities.com/ace_on_mark9909/transmission.htm

From the graph, it looks like there is a turning point

at a = 1, corresponding to T = 1, and slowly goes to

zero, as a -> infinity

By a -> infinity, we can say that the potential height

-V' approaches -infinity.

But, if the potential at x = 0, changes so sharply as

in approaching infinity, the graph shows T = 0, then,

it means that if I were to replace a particle with a

ball/human and is to approach this potential it is

almost likely to be reflected back...

Is there anything wrong with my maths? If not, how do

you interpret this result?

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# Transmission coefficient and the reflection coefficient

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