In reply to Dawin123
Talking about proportional responses. Nonetheless, I am going to point out that no pure classical mechanics can solve for a photon fluid, known as the ultraviolet catastrophe. A problem which was solved by Planck's law, which treated each electromagnetic mode as a quantum...
I must say I am intrigued. Those are beautiful descriptions, and they are often sparse in a Thermodynamics book.
Either way I believe solving this problem cannot be by means of Thermodynamics alone, as the temperature of the cosmic background radiation is not due to a fluid, or any classical...
ok there's one detail that I have ignored that may have been what you were looking for. wave mechanics failed to comply with the relativistic energy. at the time dirac solved this by introducing matrices that solved the wave equation if inserted, instead of just the single wave function. for...
i really really think its obvious. for example for the stern-gerlacht experiment, you know the state of the initial particle (spin) as you prepare them in a particular way, and you know the state will change because they will go through the potential, therefore state is time dependant and is...
the mathematician ofcourse, tends to put hard problems in terms of problems that have been solved before. There is a combination of theories that goes behind why you can solve the wave equations in this manner, and going back to the beginning of what I was trying to say, it really boils down to...
I was under the impression, that quantum measurement of the first kind would leave the wave function collapse. clearly that's not the case.
in a quantum non-demolishing experiment you may reverse the change you had done to the system to leave it back in a superposition state. Information taken...
i may have confused cosmic background radiations with vacuum fluctuations. either way even if you manage to get rid of the cosmic radiations, you cannot get rid of the nonzero vacuum fluctuations ground state energy. btw temperature is another measure of the internal energy.
diagonalising a matrix is equivalent to rearranging its eigenbasis such that they are all linearly independent, and thereby equivalent to solving a set of differential equations coefficients to find unique solutions for each one.
for more information you may refer to a mathematical methods for...
I think it is important to know what we know exactly as we do the calculations, rather than simplify them just so that you understand in classical terms, because there is really no alternative. If classical mechanics really explained everything, then there wouldn't be so much success attached to...
The Heisenberg picture is the one that is physically realisable in real experiments. In reality the particle is moving through some potential which leads to changes in it's basis and we can do experiments to find out what that potential looks like. we can make some guesses about what the state...
That's not true. the third law states that zero kelvin is unreachable. Quantum mechanics confirmed this by investigations of the Casimir effect: there's no obligation that you read this obviously, unless you find it interesting:
http://en.wikipedia.org/wiki/Casimir_effect
Essentially the ground...
a rotation in 3 space, is a transformation upon which the length of the initial vector is unchanged.
a Lorentz transformation, is a unique transformation in 4 space that preserves the length of the 4-vector of any line in 4 space, and it necessarily holds if there is a limit to translational...
in the Heisenberg picture, the states are constant in time, and the evolution is carried on by the operators, thereby allowing you to put the equations in tensorial form (matrix), as the gradient of a state tensor is always of the second rank, this simplifies the calculations provided you know...
I may have deviated a bit from the main theme here. The idea is that weak measurements may leave the system in the original eigenbasis, since they operate via a different channel, and have much different lifetimes and linewidths. Essentially avoiding the collapse of the wave function.
Quantum non-demolition measurements corresponde to the case of acting with an operator which is hermitian and commutes with the Hamiltonian (or another operator of the system). In this case both operators can have simultaneous solutions. the system can therefore coexist in both states at the...
If you want to know in detail how to solve these problems, you need to read about partial differential equations, which is a whole subject in maths. else you're going to have to believe in a lot of hocus pocus that the books throw at you. Memorising the key bits is the best way to pass the...
setting the LHS of 5 to 3 will give you the final solutions on your last step of workings, provided we put in R that we have deduced using boundary conditions in the LHS. unfortunately the notation in your book, for some reason does not include R in the wavefunction formulae. essentially the...
hello my friend. i am going to answer very specific questions, because you seem to be very lost and this is a very advanced area. whether you understand it or not depends on whether you have done a lot of previous work or not...
The solutions that we dreamed up at the start for f, are only...
to simplify the discussion, let us take the case of an ideal glass that cannot absorb any photons. on the microscopic level, the E.M. field in the medium experiences a different group velocity due to the presence of charged particles etc... the relative motion of the present particles will not...
i cant edit the bit that i wrongly talked about angular velocity. v = r x ω. so at larger r, v will be larger since ω is the same in circular rotation. v is the linear velocity of each point pointing straight like a tangent on the circle
Since you insist, I will try to explain this more clearly. First to try and clear up some ambiguities in your very own description. here is a diagram that will help clarify what I talk about:
http://www.maths.surrey.ac.uk/explore/michaelspages/Spin.htm
It is CRUCIAL, that you specify which...
Glad I could help. I think you are quite right that the magnetic resonance book by Hore is more chemistry oriented. It sort of avoids making mathematical representations. Nonetheless it is quite strong in its description. Most books on NMR I find do not make the crucial connection between...
yes i was perhaps pressing on a point not quite relevant to your question. any way the bracket needs to be expanded by a multinomial expansion, or a binomial expansion if you prefer that way.
here's some help on how to do those:
http://en.wikipedia.org/wiki/Multinomial_theorem
You're kind of missing the point here. You cannot perform a division operation on a vector.
<ψ|(1/X^2)|ψ> is not mathematically defined. The object 1/<X^2> however makes more mathematical sense.
Any Hamiltonian with a potential quadratic in position coordinates, and non relativistic kinetic...
the division process is not defined for operators. unless you mean inversion which gives a rather simple answer, knowing that the lowering and raising operators are each others inverses. If you just want to know what is the inverse of the expectation value of x squared, that isn't too difficult...
I'm afraid there isn't any one book that I know of that satisfactorily describes all of these phenomena. But there are good ones I have come across for example NMR is described pretty thoroughly in "Nuclear Magnetic Resonance" by PJ Hore. For STM, "Nanophysics and Nanotechnology" by E. Wolf has...
it is not quite appropriate to think of cross sections of particles in a material to be directly related to the resistance. the number density will come into play and without a clear knowledge of the composition, it will not be possible to formulate resistance. Instead one thinks of the average...