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That was helpful. Thanks. I learned that this type of integrals are called iterated integrals. For this type of integral the order is important particularly when the integrand is not continuous on the domain of integration. Then I found a theorem called Fubini’s Theorem. I understood that we...

Yes. it seems good. But I want to ask: for this type of integral does the order matter? I should start by integrating w.r.t. r2 first or it is optional?

I want to do this integral in the picture: where r1 and a are constants. I know I can integrate each part separately. There will be an integral with respect to r2 multiplied by integral with respect to theta2 and the last one with respect to phi2. But the term under square root confuses me. Can...

Sorry, the electron's orbital momentum points in the same direction of the magnetic field. Thanks!

Yes the period the same. But The direction of the angular momentum is parallel to the direction of the magnetic field, then the electron orbital momentum vector should point to the opposite direction?

I though the periodic time and the radius of the rotation are affected by the relativistic motion, so the periodic time from the point view of the electron will be different from the point view of the proton.

I was reading about Compton scattering. I have a question I did not find an answer for it in the book (Concepts of Modern Physics-Sixth Edition-Arthur Beiser) or in the internet search. My question is: Is the incident X-ray beam, with the original wavelength, detected at different scattering...

I was reading about characteristic x rays. I have a question I did not find an answer for it in the book (Concepts of Modern Physics-Sixth Edition-Arthur Beiser) or in the internet search. My question is: How do the atom in the target (in the x ray production experiment) go to the normal state...

I tried but the results did not convince me!

why smaller cross-sectional area increases the resistance of a conductor?

Hello, I am looking for the best book to study solid state physics for begginers. Some one recommended Gerald Burns's book: Solid State Physics. So, what is your opinions about this book if anyone has read it before. Or there are other books better?

He said he is going to use a process of successive approximations, I am not familiar with the "asymptotic expansion" so I can not tell if this what he did

In equation [9.15] ##c_a(0) = 1## this is before the perturbation (at time ##t= 0##) no transition happened yet and the particle still in the upper state ##a##. But equation [9.17] after perturbation at time t and ca(1)(t) = 1 is the first-order correction. I understand that the zeroth-order...

He used a process of successive approximations, so for this two particle system the particle starts at state ##a##, then at time t=0: ca(0)=1 and cb(0)=0. If there were no perturbation the system will stay there forever, so we can say the zeroth- order terms are: ca(t)=1 and cb(t)=0. To...

I was reading in the Book: Introduction to Quantum Mechanics by David J. Griffiths. In chapter Time-Dependent Perturbation Theory, Section 9.12. I could not understand that why he put the first order correction ca(1)(t)=1 while it equals a constant.

I only studied two spin half particles from the book Introduction to Quantum Mechanics by David J. Griffiths. I do not know if this enough For example see the attached picture.

for S^2 I will say: S^2=(S1+S2)^2= (S1)^2 + (S2)^2 +2S1.S2 where S1.S2=Sx1Sx2+Sy1Sy2+Sz1Sz2 and add all these 4x4 matrices together to find S^2

For Sz: I added the two 4x4 matrices together: Sz1 + Sz2 and I got 4x4 diagonal matrix with diagonal elements: hbar, 0, 0, hbar.

The problem is I am not familiar with this type of product using this symbol: \otimes ! So will it be wrong if I used the way I described above a got the correct matrices?

Yes this what i mean.

I am looking for 4x4 matrices.

I have this homework: consider the case of two spin half particles. Use the basis: |++>, |+->, |-+>, |--> to find the matrices representing the operators S^2 and S_z. My idea for the solution for S_z is: S_z=S_z(1)+S_z(2) where S_z(1) is the operator for the first particle ... etc So I...

It worked now, but I equated the the first order of ##\epsilon## (in the left side) with the zeroth order of ##\epsilon ## (in the right side) because the right side is multiplied by ##H^{'}## which is small (of the same order of ##\epsilon##). For example for the first order of ## \epsilon## i...

I was reading in the Book: Introduction to Quantum Mechanics by David J. Griffiths. In chapter Time-Dependent Perturbation Theory, Section: Two-level system. Every thing was fine till He said He will solve this equation: by a process of successive approximations. I have no idea what this...

I was reading in the Book: Introduction to Quantum Mechanics by David J. Griffiths. In chapter Time-independent Perturbation Theory, Section: Spin -Orbit Coupling. I understood that the spin–orbit coupling in Hydrogen atom arises from the interaction between the electron’s spin magnetic moment...

It is clear now. It seems to me that I need to educate myself and study more in linear algebra. Thank you for your help!

Can we say that if the operator is Hermitian then: <ψ| A |Φ> =<Φ| A |ψ>*= a <Φ | ψ>* = a <ψ | Φ> ?

I am not sure if this is true or not.

If A is Hermitian then the eigenvalue (a) is a real number.

Summary:: Operator acts on a ket and a bra using Dirac Notation Please see the attached equations and help, I Think I am confused about this

Thank you, that was helpful and nice.

Thank you all for useful replies.

I know that the resistance of an ohmic conductor increases with length because the electrons going through the conductor must undergo more collisions in a longer conductor. But why decreasing the cross-sectional area of the conductor also increases the resistance of a conductor?

While reading in the book of Introduction to Quantum Mechanics by David Griffith in the section of Fine structure of Hydrogen: spin- orbit coupling, he said that the average value of S operator is considered to be the projection of S onto J. I could not understand why he assumed that. please...

Thank you all for the explanation and useful discussion.

This new information for me! Thank you!

Thank you for the useful explanation.

Hello, In the section of Magnetic Force on a Current- Carrying Conductor in the book of College Physics by Serway, it is written that the Current- Carrying Conductor in a magnetic field deflects because the magnetic force on the electrons transfers to the bulk of the wire due to the collisions...

I was wondering which cleanroom ISO class is suitable for liquid crystal research?

Thanks for your explanation. what about the orbital velocity of the electrons around the nucleus?

Hi every one, In Compton effect I understand that the electron is considered free electron because the energy of the incident photon is very much larger than the binding energy of the atomic electron. But iam not sure why the electron is considered to be at rest (v=0). please help. Thanks.

Thanks, It is clear now.

Hi every one I have three simple questions: what causes Blackbody radiation? what does Planck meant by the oscillators? why the Blackbody radiation is continuous while the emission spectra of atoms (gases) is discrete? I know that the discrete emission spectra of atoms was explained by Bohr's...

I understand that diffusion is the movement of molecules from a region where concentration is high to one where it is lower. This happens due to the molecular agitation which leads to frequent collisions and hence scattering of molecules. But I do not know what is effusion. Any help? Thanks

I think I am confused: is the average velocity calculated using Boltzmann distribution is similar to, for example, measuring the velocity for one molecule many times and take the average?

Hello What is the meaning of the average velocity of gas molecules calculated by Boltzmann distribution (in kinetic theory of gases)? Does all molecules have the same average velocity?

you have three different types of atoms each one has different atomic weight.