I can see that some of the exponents have vanished so the integral which gives me problems is
- \int dr^{3} dr'^{3} \frac{n^{2}}{|r-r'|}
which in scaled coordinates can be written as
- \frac{3}{4*pi}\int d\tilde{r}^{3} \frac{1}{\tilde{r}}
I have to show that the hamiltonian for a homogeneous system can be simplified in scaled coordinates.
The first two terms I can convert to scaled coordinates <T>+<V> whereas I have some trouble for the last term
-½* \int d³r d³r' \frac{n²}{|r-r'|}
where n is the density. The scaled...
Hi,
I am approximating a proton transfer from one water molecule to another. I would to have a quantum mechanical description of the proton transfer as a wavefunction. So I have approximated a "transition state" and use this as a harmonic potential. Then I get some energy values around this...
I think I have solved it by combining the three pairs into unique pairs
{1,1},{2,1},{2,-1} having these constraints on the eigenvector equation it is possible to determine a eigenvector for the matrix A fulfilling both A and B.
The particle is in a one dimensional well with V(x) = 0 for o <= x <= a and otherwise it is infinity. Is it a linear combination between the two states ?
Again thanks very much
Hey,
I have a normalized wave function
PSI = c_1 psi_1(x) + c_2 psi_1(x)
where c_1 and c_2 are constants with the eigenfunctions equal to ground and first excited state. The average energy of the system is pi^2hbar^2/(ma^2) - what can one deduce about the constant and how?
Thanks...
Hey,
I have two matrices A and B which commute. For A I have 1,-1,-1 and for B I have 1,2,2.
I am asked to find the quamtum number for the three states. How to find the quantum states from the eigenvalues. It is further said that it is possible to find the eigenvectors from the quantum...
Maybe I have expressed the problem badly. a is the annihilation operator and a+ is the creation operator. I have a two state system |1>, |2> with a wavefunction (psi) = |1> + |2>. My problem is to perform the multiplication in order to find the expectation value:
(<1| + <2|)(a + a+)(|1> +...
Hey,
I am calculating the expectation value of the position x. I have the wave function
psi(x) = |1> + |2>
so I use the equation <x> = <psi|(a+a^+|psi> to calculate the mean value. So I get
(<1| + <2|)(a+a^+)(|1> + |2>)
which I reduce to
<1|a|1> + <1|a|2> + <2|a|1> +...
Hey,
I plot three equations than, a straight line k/k0 and a sinusoidal where I disregard the areas not allowed by the tan-function. I get a lot of intersections of k - than how to convert these to energies of V0 ?
Hope it is okay I ask again - thanks
hmmm - I have read the notes and they make some things more clear but I don't get how I can deduce V0 knowing that there should be exactly two steady states without En = Pi^2 hbar^2 n^2 /(2*m*a^2)
Could one be a little more specific, please.
Hey,
An electron is in a finite square well of 1 Å so the question is to find the values of the well's depth V0 that have exactly two state ?
How to proceed with this - finding the eigenvalues En = \hbar^2\pi^2 / 2ma^2
Thanks in advance
Hey all,
I am computing the probability that a particle in an infinite well has the momentum P in the ground state(0,a). So I start by calculating the wavefunction for the particle sqrt(2/a)*sin(pi*x). Than the probability can be calculated as
P(p) = |<p|psi>|^2. How to find <p| Fourier...
Hey,
A Hamiltonian has 3 eigenkets with three eigenvalues 1, sqrt(2) and sqrt(3) - will the expectation values of observables in general be period functions of time for this system?
I don't know how to procede?
Thnaks in advance
hmmm. I get that the probability for the three states is 1/3
P = |<a|a>|^2 for each of the vectors. So the probability for measuring the same state for two particles can be calculated using conditional probability ?
Thanks for your reply
Hey,
I am a little confused with this system 1/2 particles spin at t=0
|PSI(0)> = 1/sqrt(3) (|+>_1|+>_2 + |+>_1|->_2 + |->_1|->_2
the values of S_1z and S_2z are measured at t=0. Then I have to calculate the probability that the same value will be found for the two particles.
Any...