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    What book is highly recommended as a tensor textbook?

    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...
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    [Plasma physcis] fluid equation

    Thank you for sharing me. Then i'll ask you what is the good plasma physics textbook which is good combination with Chen book? did you get any idea?
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    [Plasma physcis] fluid equation

    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...
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    [Q]Is field made by Polarization different from external field?

    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...
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    Do you have any recommendation of book involving mathematical physcis?

    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...
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    [Q] Do you understand what is numerical aperture and f number?

    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...
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    [Q] The way of phase shifting of reflection light

    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...
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    [Q]Queation about Photon and Electric discharge.

    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...
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    [Q]Do you know about exact form of Group velocity and meaning of Group Delay?

    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'...
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    [Q]How can i draw real graph from complex function?

    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...
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    [Q]What subject is required to learn String-Theory

    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...
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    [Q]Hamiltonian of many body problem.

    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...
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    Questions about Normalized Eigenfunc, Probability & Hamiltonian

    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!
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    Questions about Normalized Eigenfunc, Probability & Hamiltonian

    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...
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    [Q]Question about harmonic oscilator

    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?
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    [Q]Question about harmonic oscilator

    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...
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    Parity Operator: Revealing Function Parity & Its Role in Conservation

    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?
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    [Q]Conserative theorem and parity

    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?
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    Parity Operator: Revealing Function Parity & Its Role in Conservation

    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...
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    Parity Operator: Revealing Function Parity & Its Role in Conservation

    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...
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    [Q]Conserative theorem and parity

    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...
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    [Q]Time deviation of expectation value

    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} =...
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    [Q]Expression of Group velocity in QM

    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?
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    [Q]Eigenfunction of inverse opreator and another question.

    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?
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    [Q]Different interpretation of same wavefucntion.

    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...
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    [Q]Eigenfunction of inverse opreator and another question.

    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...
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    [Q]eigenfunction of position operator and negative energy

    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') ...
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    [Q] Time uncertainty and particle energy similar to photon

    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...
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    [Q]Analytic function of operator A

    Ya I now your way, but How can i deal with A\varphi^n showed in product of f(\varphi) expansion and g(A) expansion
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    Understanding Energy Operator in Time-Dependent Schrodinger Equation

    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...
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    [Q]Analytic function of operator A

    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...
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    [Q]differential equation of mechanics.

    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.
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    [Q]differential equation of mechanics.

    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...
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    [Q]Degeneracy and Commutability

    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.
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    [Q]One question about Magnetic boundary conditions.

    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...
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    [Q]Some confusing about Dirac Delta Function

    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...
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    LaTeX [Q]Why does latex code fail to post fomula now?

    Thank you~i didn't know that how inconvenient i am without latex. Please be hurried to install latex server!
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    LaTeX [Q]Why does latex code fail to post fomula now?

    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?
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    [Q]Some confusing about Dirac Delta Function

    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...
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    [Q] square of 'sinc function' integral

    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) =...
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    [Q]Momentum eigenstate normailization

    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'
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    [Q]Momentum eigenstate normailization

    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...
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    [Q]Momentum eigenstate normailization

    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]...