# Search results

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

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...
3. ### 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...
4. ### 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 +...
5. ### Self adjointness and domain

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...
6. ### 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...
7. ### 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...
8. ### 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)}...
9. ### 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}...
10. ### Adjoint of commutator

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...
11. ### 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)...
12. ### Relation for Inner Product with States from a Complete Set

Hi. I've found the following relation (in a book about the qm 3-body scattering theory): <\Omega^{\pm}^{\dagger} \Psi_n|p>= ... = 0 where |p> is a momentum eigenstate. So it is shown, that the inner Product is zero. Then they conclude that \Omega^{\pm}^{\dagger}|\Psi_n> = 0 because the...
13. ### Addition of angular momenta

hi everybody. \textbf{J}_1 and \textbf{J}_2 are angular momentum (vector-)operators. In many textbooks \left[\textbf{J}_1,\textbf{J}_2\right] = 0 is stated to be a condition to show that \textbf{J}=\textbf{J}_1+\textbf{J}_2 is also an angular momentum (vector-)operator. But what is meant...
14. ### Delta potential barrier in a box

hi,... i unfortunately couldn't find a solution to this problem although it seems like a classical textbook problem... how can i solve the (time independent) schroedingerequation for the following potential V(x) = \infty for x<=-1 V(x) = a\delta(x) for -1<x<1 V(x) = \infty for x>=1 so at x=0...
15. ### Commutator relations for the Ehrenfest Theorem

Hi there,... For a derivation of the Ehrenfestequations i found the following commutator relations for the Hamilton-Operator in a book: H = \frac{p_{op}^2}{2m} + V(r,t) and the momentum-operator p_{op} = - i \hbar \nabla respectively the position-operator r in position space: [H,p_{op}]...