# Search results

1. ### Eigenvalues and eigenkets of a two level system

Hilbert2 Thank you for responding. I wrote the Hamiltonian as: H11=a H12=a H21=a H22=-a Where H11,H12,H21,H22 are the H matrix components (sorry, I could not figure out how to writhe it as a matrix with this Latex Reference). Solving Det(H-λI)=0 I got that the eigenvalues are...
2. ### 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...
3. ### Momentum eigenvalues and eigenfunctions

-ih (x(\partialz\\partialy f(r)+z \partialf(r)/\partialy)-y(\partialz\\partialx+z\partialf(r)\\partialx))=-ih (xz\partialf(r)\\partialy-yz \partialf(r)\\partialx)=-ih (x\partial\\partialy-y\partial\\partialx)zf(r) Which is the same as the initial expression. What am I missing? Thanks
4. ### 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...
5. ### Harmonic Oscillator

I used the book "Fundamentals of Quantum Mechanics for Solid State Electronics Optics" - C.Tang Here is the link to the book :http://en.bookfi.org/book/1308543 [Broken] (page 79 (pdf)). Using the a+ and a- in the link you gave I get: <n|x|n>=\sqrt{\frac{h}{2mw}}<n|a-+a+|n> Now using...
6. ### 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...
7. ### 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...
8. ### 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...
9. ### 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.