Lx,Ly,Lz are not degenerate, as is L**2. To get two states with the same Lz=m, one must use two different values of l, hence these two states are not degenerate. Work out the matrices for L=2,3,4, and see directly the lack of degeneracy of the Li operators.
Regards,
Reilly Atkinson
Think of the delta function, with positive lambda, as a very narrow, deep potential well. Use your common sense and experience with the potential well to get the appropriate general form of the solution.
Regards,
Reilly Atkinson
Not so. There is absolutely no evidence that I, or you, or most anything can be in two or more distinct places at the same time. The joint probability that I can be in Seattle and Chicago at the same time is zero; any theory that describes Nature must honor this fundamental property of things...
Velocity is just the time derivative of the coordinate vector. If X is the x coordinate, then
V(X) = dX/dt = -i [X,H], the Heisenberg Equation of motion for the x position coordinate. With a conserved NR system, V=P/m, where P is the momentum operator, and m the mass.
The Dirac eq. is...
Faradave -- There's a good reason why the concept of photon has survived for over a century -- the concept is immensely useful, spanning many branches of physics, and it passed many tests with flying colours. Simply stated, there is no reason to challenge the idea of a photon -- there's no...
Take the FT of your first eq, and get K(E,p) = 1/(E-p*p) -- I'm dropping constants, except those that are really important.
Now get K(x,t) by inverting. So, K(x,t) == Integral dE dp{exp(-iEt +ipx)/(E-p*p)}. Do the E integration first, to handle the pole, push it below the E axis -- add...
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The second formulation, apart from the missing h bar, and the first are really the same. But, the latter form was used prior to Dirac to define Green's functions, and the techniques for solution are somewhat tedious -- see any E&M text written before...
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Not true at all. E&M allows various gauges for potentials, but not for forces. Now, experiment demonstrates that charged particles, moving slowly, exert Coulomb forces on each other. Thus, no matter what gauge is involved, there must be a Coulomb potential to...
Why is it the case that two or more fermions cannot be in the same state?
Why does the Dirac Eq. work?
Why does the Rosenbluth cross section for electron- proton scattering work?
Why does force cause acceleration?
Good physics allows generalizations; QM does so in spades. The ultimate issue...
Read Heisenberg's The Physical Principles of Quantum Theory for an elegant, physically based explanation of the HUP. The trick, of course, is to take a mathematically sophisticated and abstract idea and ascribe physical reality to that idea -- Heisenberg does this in a masterful fashion.
Hello...
If gamma is independent of theta, LET Z=COS(THETA). Then the equation becomes
(L^^2 -E)W= g(1-z^^2). Take matrix elements to get l(l+1)W(l) = < l |g(1-z^^2)|W>, where g is constant and |W> is the state vector. The right hand side will be a linear expression in W(l+2), W(l+1),W(l), W(l-2)...
If you want to know what a photon looks like, then you must see it. And, virtually all methods of "seeing" a photon result in the destruction of the photon -- or substantial modification thereof. That's how our visual system works; photons create photo-dissociation currents in rods and cones...
No, this is not right. To see this, take two particles with equal masses and no spin, moving in opposite directions, interacting by means of a 1- D "central" force(depends on the difference in coordinates, |x1 - x2|), say a potential well of finite extent. Then, of course, you can translate...
By definition, a solution of the time independent SE is just that. Consider an isolated hydrogen atom, in its ground state. Taking isolated to mean no interactions, implies that the atom will stay in the ground state forever -- this could almost certainly apply to very sparse hydrogen gas in the...
Think about throwing two baseballs from x=y=z=0. Throw many times in any direction you want, then you will have an event space, of ball1 at r1, and ball 2 at r2. As in(let z=0)
Ball1 Ball2
Throw
1 (5,2,0) (3,7,0)
2...