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...
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...
-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
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...
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...
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...
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...
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...
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.