Recent content by Catflap

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    Harmonic oscillator Hamiltonian.

    I would just ask people to read what I've actually said - not what someone else may have said about what they think I might have been asking.
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    Entanglement and interference effects

    Now wait a minute - you only get one shot at performing a measurement on a member of an entangled pair. What you get may depend on it's entangled state but you can't tell that. All you get is a result to the experiment you performed. You can't tell the difference between a tangled and untangled...
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    Entanglement and interference effects

    In reply to the OPs last post :- Well, it might - it probably does - that depend on the nature of what you are measuring. But the point is - you have no way to know that whatever 'shows up' has any significance or is in any way related to the electron having once been part of an entangled...
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    Entanglement and interference effects

    The question is very unclear. A spin singlet state is a definite state. In that sense, it's already 'collapsed'. In fact any quantum system has to be in some state or another at all times and is therefore always in a collapsed condition. The whole point of the EPR conjecture was to try to...
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    Harmonic oscillator Hamiltonian.

    I'm not talking about nature deriving anything from anything else. That's a bizarre idea. I'm talking about a specific mathematical 'proof' offered in physics textbooks. The problem given is to come up with a value for the Hamiltonian of the HO consistent with the concept of state vectors...
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    Entanglement and interference effects

    Yes, but since you have no way of knowing what the result was at B, it makes no observable difference to any measurement you make at A. If I give you that the result of a spin experiment was 'up' can you tell me if that was a random value from a just-collapsed wavefunction or an inevitable...
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    Harmonic oscillator Hamiltonian.

    That's just H + h/2 plus H - h/2. :) My point is that the classical H is an approximation to the quantum version, which is actually H_classical + h. You can't take an approximation and use it to derive the correct result. The textbook argument somehow suggests that the QH is derived from...
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    Is Schrodinger's cat experiment a paradox?

    It was a joke. But it illustrates a basic concept. Any interaction between particles represents an 'observation'. The world proceeds between interactions in a state of uncertainty, which is resolved when the result of the interaction 'happens'. It was probably the worst joke in the history of...
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    Harmonic oscillator Hamiltonian.

    A*A = 1/2h(x-ip)(x+ip) = x2 + p2 + i(xp-px) Classically the imaginary term is zero so you have A*A = x2 + p2 = H This gives the result you would expect classically and the lowest energy possible is zero. In QM, the commutator has the value ih/2. so that the imaginary term now has a value of...
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    Harmonic oscillator Hamiltonian.

    I know I've seen this point about roots discussed somewhere but I can't for the life of me remember where. I'm hoping someone can point me the right direction. Here's the situation:- The standard derivation of the quantum HO starts with the classic Hamiltonian in the form H = p2 + q2...
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    What is the pure imaginary number in Dirac's Principles of QM?

    I see, The real part of the expression involves D-1 the imaginary part involves D multiplied by some factor With the result of the operation D being close to unitary, the real part becomes some small fraction dominated by D, while the imaginary part becomes something dominated by the other...
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    What is the pure imaginary number in Dirac's Principles of QM?

    It's an operator related to displacement such that a displaced ket relates to the original ket by some operator D. i.e. |Pd> = D|P>. If δx is an infinitesimal displacement from the initial position, then from physical continuity a displaced ket should tend to the original ket so that the...
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    What is the pure imaginary number in Dirac's Principles of QM?

    That's the problem. D is an operator, so I have D+iDγ - not the same as D + iaγ where a is pure number.
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    What is the pure imaginary number in Dirac's Principles of QM?

    In Principles of QM by Dirac, 4th Ed page102 he gives the following:- Limδx→0(Deiγ-1)/δx = Limδx→0(D-1+iγ)/δx given that the phase factor tends to 1 in the limit I'm stuck here. My grasp of maths is pretty weak and I can't see how the pure imaginary number arises. Any help would be...
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