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  1. thariya

    A Quantization of the electric field inside a box

    Hello all, The second quantization of a general electromagnetic field assumes the energy density integration to be performed inside a box in 3D space. Someone mentioned to me recently that the physical significance of the actual volume used is that it should be chosen based on the detector used...
  2. thariya

    A Independence of Operator expectation values

    Thank you for that reference! And thank you for the offer of further discussion! I will take some time to go through your paper and will definitely take you up on that offer.
  3. thariya

    Calculus Resources for learning multivariable calculus

    Happy to help! I don't quite recall a textbook for this. I see a couple of suggestions have come in for that. Hopefully one of them will suit your need!
  4. thariya

    Calculus Resources for learning multivariable calculus

    https://ocw.mit.edu/courses/mathematics/18-02-multivariable-calculus-fall-2007/ This is where I first learnt it close to 10 years ago. The lectures are a tad old but I think they are excellent assuming you would have the patience to go through it all. It is quite worth it if you do. I have...
  5. thariya

    A Independence of Operator expectation values

    Thanks for this! I think I will go the Gaussian approximation route. Wick's theorem doesn't quite help me since my operators(ladder operators) are actually already normal ordered and their individual operator expectations are not zero. I don't see how I could reduce that using Wick's theorem...
  6. thariya

    Finding the acceleration of a block of ice on a ramp

    Yes, my bad. I did it in my head and forgot an extra factor. ##m_B## shouldn't cancel out in this case. Sorry about that fellas. It actually does depend on the ratio of the two masses.
  7. thariya

    Finding the acceleration of a block of ice on a ramp

    First, I would mark down the directions of the accelerations of the two objects along with the force diagram. As you said earlier, the ice block would move horizontally(with respect to the floor) so you can mark that off with an acceleration value quite easily(which would be an unknown in your...
  8. thariya

    A Independence of Operator expectation values

    Hi! I want to know under what conditions the operator expectation values of a product of operators can be expressed as a product of their individual expectation values. Specifically, under what conditions does the following relation hold for quantum operators (For my specific purpose, these are...
  9. thariya

    Finding the acceleration of a block of ice on a ramp

    Sorry but can't seem to be able to view the image you've uploaded.
  10. thariya

    I The sign of coupling Hamiltonian in CQED

    Thanks for that. I wrote down the derivation and I see what you mean. It basically depends on whether the cosine or sine waveform is used to describe the oscillating field.
  11. thariya

    I The sign of coupling Hamiltonian in CQED

    Thank you very much for the reply! Do the conventions vary based on the redefinition of the field operators ##b_k^\dagger## and ##b_k##? If what I think is correct, in one convention, the ##b_k^\dagger,b_k## is proportional to the quantized vector potential, while in the other, it's the...
  12. thariya

    I The sign of coupling Hamiltonian in CQED

    Hi all, I've always regarded the coupling Hamiltonian for a bosonic cavity mode coupled to a two-level fermionic gain medium chromophore to be of the form, $$H_{coupling}=\hbar g(\sigma_{10}+\sigma_{01})(b+b^{\dagger})$$, where ##b## and ##b^{\dagger}## and annihilation and creation operators...
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