That makes sense to me... Thank you. :) And yes, I am talking about energy levels for multielectron atoms in the Russel-Saunder coupling scheme.
But, what I am basically trying to do is to calculate the energy of excited states of some atoms without the effect of spin-orbit. Now, let's say I...
Thanks for the reply! But, in an f-shell with 3 electrons for instance, even if we assume that the 3 electrons all have spin up we still get several atomic terms. How can that be, what degrees of freedom are left when the configuration is locked and the spins of the electron is also locked. The...
Can someone explain to me why different terms arising from a particular electron configuration have different energies? For example, for carbon in the configuration 1s^22s^22p^2 three terms arise, 3P 1D and 1S. These three terms have different energies but I don't understand why. The electron...
When calculating eigenstates in the hydrogen atom one finds plenty of eigenstates with angular dependence. The s orbitals are spherically symmetric, but an orbital like 2p is not, there is some angular dependence through the spherical harmonics. But why is there angular dependence? It is a...
What exactly is it that you don't understand? Are you having trouble understanding what exactly those matrix elements are and why they are called matrix elements or is it something else?
Hey!
Could someone please explain to me what the exchange integral exactly represents? I understand the coulomb integral and the overlap integral, they have nice classical analogs. But there doesn't seem to exist a classical analog to exchange.
Thanks
Are you sure about that? I mean, the wavevector of a particle inside a barrier is complex so that we get exponentially decaying wavefunctions instead of oscillating ones, right? This means that the kinetic energy \hbar^2 k^2 / 2 m < 0 since k is complex.
Hey!
Can someone explain to me what the spin functions are? I understand that a spin up is described by a function which is often called \alpha and spin down is described by a similar function called \beta. But what are these functions? What do they look like and what parameters do they take...
Wouldn't a discontinous wave function imply abrupt changes in probability density? How can that be physical? I mean, if there's a certain probability for a particle to be at location A there would be a discontinuity in the probability of being in a location A' immidiately adjacent to A.
Hey!
In deriving the WKB approximation the wave function is written as
\psi \left( x \right) = exp\left[ i S\left( x \right) \right ]
Now, in some of the deriviations I've seen, the function S(x) is expanded as a power series in \hbar as
S(x) = S_0(x) + \hbar S_1(x) +...
You have to stop thinking about the electrons and photons as particles. They are quantum particles, and exhibit both wave like and particle like properties, and this enables them to interfere with each other like in the double slit exp.
Quantum physics does not try to say anything about what...
Density of states??
According to C. Kittel the density of states is the "number of orbitals per unit energy range". Alright, that's fine, but what exactly does this mean? I can understand the calculations, finding the totalt number of states by considering the fermi sphere and the volume of a...
It depends on what you define as zero potential energy. When the electron is located at a point infinitely far away it's potential energy is defined to be zero and the electron is free and not bound by the nucleus. As the electron moves closer to the nucleus it loses potential energy (the...
Well, what I want to do is derive the minimum energy of the harmonic oscillator. I start with:
<E>=\frac{<p^2>}{2m} + \frac{1}{2}m \omega^2 <x^2>
...and use the fact that:
(\Delta x)^2 = <x^2> - <x>^2
and
(\Delta p)^2 = <p^2> - <p>^2
To rewrite the formula for the energy...
Hey!
Can someone explain to why the energy of the harmonic oscillator must be at least:
\frac{(\Delta p)^2}{2m}+\frac{1}{2}m \omega^2 (\Delta x)^2
I mean, \Delta x and \Delta p represents the uncertainty in the position and momentum, and therefore it does not really have anything to do...