As it turned out. Al lthe equations were correct, but I inputed the wrong numerical values in my calculator. At the end I inserted equatioins in C programming language and it calculated everything perfectly.
At this point I managed to calculate all the coefficients, but probably they are wrong. Here is the entire calculation. If anyone spots any errors please let me know.
I read about the Steinharts-Hart's equation here and I decided to try and calculate the four coefficients of the extended Steinharts-Hart's equation:
$$\frac{1}{T} = A + B \ln(R) + C \cdot (\ln(R))^2 + D\cdot (\ln(R))^3 $$
Where T is a temperature and R is a resistance of the e.g. NTC...
After some algebra i did get the equation which gives the ratio between ##A## and ##E##:
$$\frac{A}{E}=\frac{e^{iLd}}{2LK}\left[ K^2 \cosh(iKd)-L^2\sinh(iKd)+KLe^{-iKd} \right]$$
I am a bit worried because i have a complex number in the hyperbolic cosine and sine. Is it still possible i am on...
I found a nice detailed algebra explanation for the case ##E < E_p## here (he is solving the system of eq. using matrix form - this is what i am not so familiar with). I am almost satisfied now. But i still have to find the algebra for ##E>E_p##... If anyone knows any similar sites please post a...
He just describes the result and doesn't do the algebra. He only posts the final equation for the tunneling effect (##E<E_p##) and scattering problem when (##E>E_p##). Same level of detail as Wikipedia.
I would prefer to get my hands on the cases when ##E>E_p##, ##E<E_p## and not the extremes like ##E\gg E_p##, ##E\ll E_p##. I was only trying to derive the extreme epproximation because i didn't know how to do it properly i guess...
I know, but i haven't found any derivation (in any of the books i have read) for the case when ##E>E_p## and not ##E\gg E_p##. Noone does the hard part - the algebra.
Good to know that i am at least on the right track. But do you think my approximation ##E \gg E_p## is a bit too idealistic - because i have ##E=10eV## and ##E_p=8eV##. A bit idealistic I would say...
I will chech this for sure. I hope i get some more detail. Is there any book which shows...
Homework Statement
Homework Equations
I know that energy mentioned in the statement is kinetic energy so keep in mind when reading that ##E\equiv E_k##.
In our case the kinetic energy is larger than the potential energy ##\boxed{E>E_p}## and this is why stationary states for the regions 1...
Thank you.
But can you explain to me why don't we generaly use the rest energy when dealing with a classical approximations. In books everyone explains the rest energy but what it really is? I mean i know how to calculate it and whatsoever but when does it appear and why do we have to take...
Homework Statement
On our modern physics class e did a problem:
At first i said: "Oh i know this!" and solved the case like this.
Homework Equations
Lorentz invariant: ##E=\sqrt{{E_0}^2 + p^2c^2}##
Schrodinger equation where ##V(x)=0##.
The Attempt at a Solution
The energy ##100eV## must be...
So there is no way to solve this except to put the transcendental equation into a program like Mathematica to return the numerical value or draw the graphs and then find the intersections.
Thank you I will tell this to the professor so he can fix it.