Thank you for the answer.
The elements of Schrodinger equation are quit familiar one to me. The equation includes hamiltonian and energy.
So, I thought it can be derived from Lagrange mechanics(or Hamilton mechanics), which has basic principle called "principle of least action", or Lagrange...
Homework Statement:: Derive Schrodinger equation
Relevant Equations:: Schrodinger Equation
I want to find the derivation of Schrodinger Equation.
Actually, I learned quantum mechanics already, but I think the proof that begins from the plane wave solution is quit ambiguous.
Because I feel...
The result equation doesn't fit with the familiar divergence form that are usually used in electrodynamics.
I want to know the reason why I was wrong.
My professor says about transformation of components.
But I cannot close to answer by using this hint, because I don't have any idea about "x"...
Yes. I only tried it about Cp value, because the van Der Waals gas's one is so complicated.
In addition, that Cp value come from
$$ \ln{\frac{⟨N⟩}{nQV}} = \ln{\frac{⟨N⟩βP}{nQ⟨N⟩}} = ln{\frac{βP}{n_Q}} $$
in Entropy term.
And fortunately, In my midterm, my professor didn't ask about heat...
Thanks!
I have checked all of my equation... And, I found several mistakes.
By your feedback, I tried it without derivative of N respective of T.
And I got a right Cp value. 5/2 Nk.
And also I will try the equation you gave me.
Really Really Thank you. :D
To find where i wrong, I tried to solve isobaric heat capacity in ideal gas.
So, I got entropy. it's the Sackur-Tetrode equation.
$$S=\braket{N} k[\frac{5}{2}-\beta\mu], when \;\mu \; is\; chemical\; potential.$$
it's same with
$$S=\braket{N}k[5/2-\ln{\frac{ \braket{N}}{(n_Q*V)} } ].$$
The...
In our class, we're using Wassermann's Thermal physics as textbook.
I always try to solve all question which included in Text book.
But sometime when I meet a problem that look like easy but actually hard, I'm so embarrassed.
This problem do also.
First, in the textbook grand potential for van...
I understood it. Thank you.
Temperature T is always positive and P is also positive. So, the integration must be positive.
In my result, the second term will be negative. But, the size of negative term is not big enough to exceed the first term.
I should check with graph.
Previous of this problem, there was another problem. that is "What is the change in Temperature of van der Waals gas in free expansion?".
I got them.
It was
C_V dT= -aN^2/V^2 dV
Then, I got
T=T0-aN^2/2VC_V
So i knew that the Temperature is decreased by free expansion in adiabatic process.
Then I...
Hello.
I'm majoring both Physics and Biology in Korea.
Usually I am not sure about my mathematical result.
So I often find solution on the Internet.
And I'm interested in Computational Neuroscience, Mathematical Biology, Thermal physics.
I'm not sure about my proof. So please check my step. I used log as a natural log(ln).
Specially, I'm not sure about "d/dt=dρ/dt d/dρ=i/ħ [ρ, H] d/dρ" in the second line. and matrix can differentiate the other matrix? (d/dρ (dρ lnρ))