Hi.
i'm actually under the department of the applied optics so I had very few change to
face the concept, tensor.
But my research topics is highly related to particle acceleator so tensor concept is need to
be understanded to go straightfoward.
I'm looking for tensor textbook...
Hi i just learned fluide equation form chen textbok
The equation is mn\left[ \frac{\partial u}{\partial t}+(u\cdot\nabla)u\right]=qn(E+u\times B)-\nabla\cdot P - \frac{mn(u-u_{o})}{\tau}. where P is pressure and last term is collision between charged particle and the nutral
I was confusing...
Hi.
It is supposed that External field imposes to dielectric matter and Polarization occurs.
Thus, Bounded volumb and surface charge are made.
My question is, is field induced by Bounded charge in addition to original(external) field
different from original field existing...
Hi, I'm very interesting about Theoretical physics, In fact, I want to learn about Particle
physics for my desire to solve difficulty.
But, when I tried to study the famous mathematical book, by afken, I recognized it very hard
to study by myself.
So, I want to know other book...
Hi, I studied concept of numerical aperture and f number
I learned numerical aperture(N.A) is measure of how much light can be entered into the
optical system, its mathematical expression is N.A = nsin\theta_m where n is
index of refraction of immersing medium surrounding lens and...
Hi, I learned optics with pedrotti optics book.
It is suppopsed that light is reflected on surface of first layer and
then tranmited wave is also reflected on surface of second layer, So there is Double Layer
incident light get there.
According to book, If two reflections are...
Hi, I just wander what hapeens if photon which energy is higher than difference of adjacent
energy levels collide with atom? How does Excess energy go? transmiting atom by form of
photon or giving motional energy to the atom?
Second Question is What does process ocurrs when enough...
Hi, It is long time to come here sine i graduate University.
Anyway, My question is whether exact form of Group velocity is \frac{dw}{dk}
or \frac{dw}{dk}|_{\bar{k}}
I want to know whether Group velocity is independent of K, propagation number
Becasue Group velocity is 'proper'...
For instance,
I have a simple eigen function such as \varphi = Ae^{ik_{1}x} + Be^{-ik_{1}x}
This is complex form which means we can't draw this function on real coordinate.
How can i draw this function? just By taking out real term of complex function?
Second question is what...
Hi,
I'm curious about What world it is, What happened to the initial world to become this state.
I'm student undergraduate and I got admission from plasma laser lab of graduate school.
But i want to learn about String-Theory. So i planed to learn relevant subject step by step.
But...
Hi
I thought Hamiltonian for two particle system is H = \frac{-\hbar^2}{2m}\frac{\partial}{\partial x_{1}} + \frac{-\hbar^2}{2m}\frac{\partial}{\partial x_{2}} + v(x)
But is it right? I just want to know This way is right to construct every hamiltonian of many
body system.
What i...
Thank you for your help I solved my first question. But How about second and third question? Anyone know about this well?
I can't imagine real meaning of the Probability current density!
Hi. I have three question. First is form of normalized momentum egien function
Liboff said that of unbounded is \frac{1}{2\pi}exp[ikx] But Why should this
form be normalized eigen function of momentum in unbounded?
Second question is whether probability density is equall to...
Thank you for your help! I'm very pleased with you. But Could you tell me how to apply chain rule of calculus on that formula? I just subsitute x = \beta\epsilon into the x of dominator to get your formula. is it right procedure?
What is more, Can you give me a answer of second question?
Hi, Finally! I reached harmonic oscilator! Congratulation!
Most of all QM textbook introduced this formula :
Time independent energy eigenstate equation is
( - \frac{\hbar^2}{2m} \frac{\partial}{\partial x) + \frac{Kx^2}{2} )\varphi = E\varphi
(1) \varphi_{xx} = -k^2 \varphi...
So, u means even that i previously know parity of function is just interpreted as operating parity operator to the function?
Is it right? Is it essential in QM?
I agree your calculation it is very insparational.
Buy how could you explane my question? f(x + \varsigma ) is translating f to left by \varsigma .
I interprete \hat{D}(\varsigma) is translating physics system to right by \varsigma
Is my interpretation wrong?
I'm studying QM with Liboff fourth edition, it contains amazing contents
But i can not agree your answer because We should know momentum operator to obtain
corresponding eigenstate and eigenvalue which is used to predict experiment.
But for parity opeator, we can not evalute...
Hi, i separated parity question from my question posted just below
Parity operator reveal parity of function such that Pf = \pm f
But In fact, in order to get parity of function f, we should already know parity of function
In that way, Why should we know Parity operator ? we already...
Hi,
I encountered three conserative theorem in textbook
One of conserative theorem is involving my question.
Liboff defined displacement operator as \hat{D}(\varsigma) = e^(\frac{i\varsigma\hat{p}_{x}}{\hbar}f(x) = f(x + \varsigma ) but is it right?
If system is displaced from x...
Hi,
You know famous equation, \frac{d<A>}{dt} = <\frac{i}{\hbar}[\hat{H},\hat{A}] + \frac{\partial\hat{H}}{\partial t} >
But liboff said if \frac{\partial \hat{A} }{\partial t} = 0 then, \frac{d<\hat{A}>}{dt} = 0
this is the proof
\frac{d<A>}{dt} =...
Hi.
We already know Group velocity is \frac{\partial w }{\partial k }
But, liboff said Group velocity is \frac{\partial w }{\partial k }|_{k_{max}} where k_{max} is wave number which probablity this value can be measured is higher than other wave number.
is it right? How can?
I don't understand why AA^{-1}\varphi = \varphi It is absolute true that
AA^{-1} = 1 But applying AA^{-1} to some function is
different matter. for example we assume A and its inverse can be matrix, function f is also matrix.
A(A^{-1}f) is not (AA^{-1})f right?
Hi
Is it possible that same wavefuction described by math can be interpreted to different
aspect?
For instance, Some wrote wave function as same as momentum eigenstate which is
normalized
But he seemed claim that it is not momentum eigenstate even mathmetical formula is same...
Hi.
Do you know eigenfunction of inverse operator, for instance \hat{A^{-1}} given that \hat{A}\varphi = a\varphi
textbook said eigenfunction of inverse operator A is the same as \varphi
which eigenvalue is \frac{1}{a}
Can you prove that?
And is it really that...
Hi, Everybody know that eigenfunction of position operator x' is \delta(x-x')
But i also knew that integral of square of current state over entire space is 1(probability)
Then, \int_{-\infty}^{\infty}\delta(x-x')\delta(x-x')^{*} dx is 1?
What is conjugate of \delta(x-x') ...
Hi i applied i\hbar \frac{\partial}{\partial x} to energy eigen state which is
evolving in time, e^{(i(kx-wt)} and i get energy eigen value \hbar w
but i was surprised it is very analoguos to energy of photon!
How can is it happened? Energy of photon is depending on time...
Hi liboff proble 5.28 says
time dependent schrodinger equation permits the identity such as E = i\hbar \frac{\partial}{\partial x} (E is operator)
But i don't understand E( is operator in this problem) can be thought energy operator
Is energy operator only H, Hamiltonian?
If E is energy...
Hi, 5.27 problem in liboff says that if g(A)f(\varphi) = g(a)f(\varphi),where A\varphi = a\varphi
I tried to solve this problem with tylar expansion.
f(\varphi) = f(0) + f^{'}(0)\varphi + \frac{f^{''}(0)}{2!}\varphi^2 + \frac{f^{(3)}(0)}{3!}\varphi^3 + ...
g(A) = g(0) + g^{'}(0)A...
I'm surprise that laplace is useful tool to solve differential problem.
For solving differential equation, What kind of method does physics student use to solve?
Please give me a list including most useful method, give me a exact mathod name.
Hi, When i solve some lagrange equation, i encountered a lot of equation of motion that
is difficult to solve for me. They are not simeple harmonic oscillator form, even they are
partial difficult equation.
How can i solve thse equation? How do you solve?
I'm curious How can other...
Hi
Liboff said that with two operator [A,B] = 0, If some eigenstate of operator A are degenerate, they are not necessarily completely common eigenstate of B.
How is it proved or where can i find proof of this theorem?
Please answer me.
Hi.
You know that B_{1n} = B_{2n} as one of the boundary condition when
magnetic field is go across from material 1 to material 2, n means direction perpendicular to
the boundary surface.
I wander this theorem is right in non-uniform field which is function of space variable r...
I see, Thank you So thank to your assistant. I can make conclusion that
Hermition operator produces orthogonal eigen function but, orthogonality only persists in
case of that domain of eigen function is infinity,
In other word, orthogonality is break up with physical restriction.(Real...
Before physics forum sever moved, latex code i wrote did well
But at this time, all latex code i wrote fail mulfunctions.
What happened? and How do i have to do?
Hi.
Recently day, I tried to solve quantum mechanics problem in liboff fourth version to prepare
graduate school.
But what make me be confused a lot is Dirac Delta Function.
One of my confusing on Dirac Delta is what i wrote below.
-One of the formula describing Dira Delta...
Hi.
I tried to solve some problem that i should get probability density with which eigenstate of
momentum is chosen after momentum measurement by using <\varphi_{k}|\Psi>
I faced some stuck integral problem such as \int_{k_o}^0\frac{sin^{2}(2x)}{2x^{2}}dx
I transformed sin^{2}(2x) =...
It means innerproduct such as <\varphi_{k}|\varphi{_{k^'}}> i described
product of this form as more general form of 'vector innerproduct in normal vector space'
Thank you so much that i found Fourier transform is included general innerproduct
in some mathematical space as l Fourier transform is just analogous to vector
innerproduct between momentum eigenfunction and statefunction. thank you.
but i have one questiong. what is hilbert space in...
Hi
I use liboff quantum mechanics textbook fourth edition.
5.25 fomula of 122 page is \frac{1}{\sqrt{2\pi}}e^{ikx}
I thought it is nomalized, but i don't know exactly why \sqrt{2\pi} is denominator.
I think it seemed to be linked Dirac-delta function [itex]...