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    Eigenvalues and eigenkets of a two level system

    1. Homework Statement The Hamiltonian for a two level system is given: H=a(|1><1|-|2><2|+|1><2|+|2><1|) where 'a' is a number with the dimentions of energy. Find the energy eigenvalues and the corresponding eigenkets (as a combination of |1> and |2>). 2. Homework Equations...
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    Momentum eigenvalues and eigenfunctions

    1. Homework Statement For the following wave functions: ψ_{x}=xf(r) ψ_{y}=yf(f) ψ_{z}=zf(f) show, by explicit calculation, that they are eigenfunctions of Lx,Ly,Lz respectively, as well as of L^2, and find their corresponding eigenvalues. 2. Homework Equations I used...
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    Harmonic Oscillator

    1. Homework Statement I need to show that for an eigen state of 1D harmonic oscillator the expectation values of the position X is Zero. 2. Homework Equations Using a+=\frac{1}{\sqrt{2mhw}}(\hat{Px}+iwm\hat{x}) a-=\frac{1}{\sqrt{2mhw}}(\hat{Px}-iwm\hat{x}) 3. The Attempt at a...
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    A particle in 1D potential well

    Hello, What does it means when a particle having mass "m" in a one dimentional potential well has the potential given by: V(x)= \stackrel{-\alpha δ(x) for |x|<a}{∞ for |x|≥a} where δ(x) is the delta function and \alpha is a constant. I understand that the well boundries have...
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    Expectation value of kinetic energy

    1. Homework Statement Given the following hypothetic wave function for a particle confined in a region -4≤X≤6: ψ(x)= A(4+x) for -4≤x≤1 A(6-x) for 1≤x≤6 0 otherwise Using the normalized wave function, calculate...
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    Projection operator

    Hello, Suppose P is a projection operator. How can I show that I+P is inertible and find (I+P)^-1? And is there a phisical meaning to a projection operator? (Please be patient I have just started with QM). Thanks. Y.