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1. Shrunk and thrown into a blender

Hi everybody, I encountered this question as an example of what a google applicant is asked: You are shrunk to the height of a 2p coin and thrown into a blender. Your mass is reduced so that your density is the same as usual. The blades start moving in 60 seconds. What do you do? It is...
2. Product of Dirac Spinors

Thanks a lot ...
3. Product of Dirac Spinors

Hi togehter. I encountered the following problem: The timeordering for fermionic fields (here Dirac field) is defined to be (Peskin; Maggiore, ...): T \Psi(x)\bar{\Psi}(y)= \Psi(x)\bar{\Psi}(y) \ldots x^0>y^0 = -\bar{\Psi}(y)\Psi(x) \ldots y^0>x^0 where \Psi(x) is a Dirac...
4. Uncertainty principle

Thanks again. But that's what i meant. It is unlikely but not impossible. And a very poor lower bound doesn't justify to call \Delta p the typical momentum. It seems as if one could conclude the mean value (which i assume is the typical value) from the standard deviation. But there's no...
5. Uncertainty principle

Thanks, but i think it's meaningless to give a lower bound and speak of typical momenta. The uncertainty can be a very small fraction of the actual momentum or vice versa, so i can't believe they meant it this way.
6. Uncertainty principle

They say: "The uncertainty principle gives an estimate for the typical electron momenta when they are confined to such a linear domain." Then they give the above formula. But all they get from the uncertainty principle is the uncertainty \Delta p which is not the typical momentum. In my...
7. Uncertainty principle

Sorry for bumping, but i can't belive that nobody who did some lectures on particle physics ever encountered this (or a similar misuse of the uncertainty principle) problem. I would be very glad for an answer. Greetings.
8. Uncertainty principle

They conclude that the momentum of the electron is \approx \hbar/\Delta x , so it surely isn't zero. They want to calculate the typical momentum of an electron in an atom, it would not be very helpful to chooce such a reference frame, because the answer would be that the typical momentum is...
9. Uncertainty principle

Hi together ... In many textbooks on particle physics i encounter - at least in my mind - a misuse of the Heisenberg uncertainty principle. For completeness we talk about \Delta p \Delta x \geq \hbar/2 For example they state that the size of an atom is of the order of a few Angstroms...
10. Representing a vector in terms of eigenkets in a continuos basis

Hi. The whole thing is rather sloppy and mathematically not very well justified by Dirac. If you have an operator A in the Hilbert space the eigenvalues and eigenkets of the operator satisfy A |a\rangle = a|a\rangle where a is an eigenevalue if you have a continuum of eigenvalues in an (real)...
11. How one can deduce the existence of antiparticles

O.k. so everything in the exponent multiplied by t except the -i is the frequency \omega. As E=\hbar \omega the negative energy comes from the negative frequency. Mhh i think i probably got it although there are many cases i remember where the time dependence was \exp(i \omega t) and no one...
12. How one can deduce the existence of antiparticles

my point is: you say that there are negative energy solutions because, as you showed, the general solution bears a plus AND a minus sign in the exponent. but it seems to me it would be the same to say the energy can be imaginary because there is an i in the exponent. i simply don't get the...
13. How one can deduce the existence of antiparticles

thank you. i also heard this statement, but it's the same story i think. only this time the sign is carried over to the paramter t instead of the energy. i'll try to make my point clear: although the solutions are \Psi(t,\vec{x})=\exp(\pm i (- E t + \vec{p} \cdot \vec{x})) you don't...
14. How one can deduce the existence of antiparticles

yes, but as i mentioned earlier, why does this sign carry over to the energy? why don't say the energy is positive but the functional dependence, to get linearly independent solutions, is exp(- ...) respectively exp(+ ...)? thanks for your help and please excuse my problems understanding that...
15. How one can deduce the existence of antiparticles

Thanks. Thats a linear superposition of the fundamental solutions i cited above, but as you wrote \omega and thefore the energy is positive and there is no need for negative energy states called antiparticles. Or did i misunderstand something? edit: Back when they dealt with the Klein-Gordon...
16. How one can deduce the existence of antiparticles

that was my point ... I know that they have been found experimentally. But it is always quoted as a great triumph of theoretical physics that antiparticles were predicted on grounds of the Klein-Gordon equation or the Dirac-Equation respectively.
17. How one can deduce the existence of antiparticles

Hi together ... I wonder how one can deduce the existence of antiparticles from the Klein-Gordon equation. Starting from (\frac{\partial^2}{\partial t^2} - \nabla^2 + m^2) \Psi(t,\vec{x})=0 one gets solutions \Psi(t,\vec{x})=\exp(\pm i (- E t + \vec{p} \cdot \vec{x})) leading to E^2=p^2 +...

Thanks a lot for the hint. So it was an error in the book. For the record: B. Thaller - The Dirac Equation. Section 1.2.2. Greetings. Tommy

Thanks, but in the statement i quoted the domain of A(t) isn't U(t)D(A) but U(t)^+ D(A) and then we have (U(t)^+ \Psi, U(t)AU(t)^+ U(t)^+ \Phi). Is this a typo?

Hi together ... I encountered the following statement: Operator A is self adjoint on D(A) then A(t) \equiv \exp(iHt) A \exp(-iHt) is self adjoint on D(A(t)) \equiv \exp(-iHt) D(A). H is self adjoint, so that exp(...) is a unitary transformation. But why does the domain transform this way...
21. Bounded Operators

Great! Many thanks to both of you.
22. Bounded Operators

hi. i'm reading "quantum mechanics in hilbert space" and a don't get a basic point for bounded operators. def. 1 a set S in a normed space N is bounded if there is a constant C such that \left\| f \right\| \leq C ~~~~~ \forall f \in S def. 2 a transformation is called bounded if it maps...
23. Driven quantum mechanical harmonic oscillator

Hi. I just calculated the quantum mechanical harmonic oscillator with a driving dipole force V(x,t) = - x S \sin(\omega t + \phi) I used the Floquet-Formalism. Then I calculated the mean expectation value, in a Floquet-State, of the Hamiltonian over a full Period T indirectly by using the...
24. Stationary Perturbation Theory

Hi together... When reading Sakurai's Modern Quantum Mechanics i found two problems in the chapter "Approximation Methods" in section "Time-Independent Perturbation Theory: Nondegenerate Case" First: The unperturbed Schrödinger equation reads H_0 | n^{(0)}\rangle=E_n^{(0)}...
25. Direct Product Basis for Interacting Systems

Great. Thanks for your answers. i hope i got it (at least partially). @Fredrik: Thanks for your rigorous explanation. But the Hamiltonian i wrote above can't be brought in this "non-interacting" from.
26. Direct Product Basis for Interacting Systems

Hi. I found in a book on quantum optics (Vogel, Welsch - Quantum Optics) and also in a lecture script the following statements. A System is composed of two subsystems (say A and B) which interact. So the total Hamiltionian is H_{AB}= H_A + H_B + H_{int}. Nontheless the states of H_{AB}...

Thanks for your replies. I found the problem. The identity only holds for the special case of creation-/annihilation-operators, where the (anti-)commutator for fermions or bosons resplectively is zero. thanks and greetings.

Hi all. I found the following identity in a textbook on second quantization: ([a_1^{\dagger},a_2^{\dagger}]_{\mp})^{\dagger}=[a_1,a_2]_{\mp} but why? ([a_1^{\dagger},a_2^{\dagger}]_{\mp})^{\dagger}=(a_1^{\dagger}a_2^{\dagger}\mp a_2^{\dagger}a_1^{\dagger})^{\dagger}=a_2a_1\mp a_1a_2...
29. Invariance of Schrödinger's equation

hi all. thanks for your quick answer. i'm going to consult landau and lifgarbagez.
30. Invariance of Schrödinger's equation

I thought i had a basic to intermediate understanding of quantum physics and group theory, but when reading hamermesh's "group theory and it's application to physical problems" there's something in the introduction i don't understand. first of all, i know the parity (or space inversion)...