Recent content by ftft

Thanks for the reply.. Yes, I meant D_2 group.. But why are the 3 axes equivalent? I thought the rule is that one principal axis in the system is chosen to define the properties of the irreps. Say we choose the z-axis to define the principal axis, B1 behaves like A2

In my understanding, in group theory the one-dimensional irrep A differs from the one-dimensional irrep B in the symmetry under rotation about the principal axis: A is when the state is symmetric and B is when the state is antisymmetric under that rotation. However, I find in the character...

I often hear scientist say that generally the effect of a weak perturbing potential on the ground state of a system is larger than its effect on higher states and that the strength of the weak perturbation on the states decrease as we go higher in energy. For example, if a weak potential is...

In group theory, what is the direct product of a symmetry group with itself? Say T*T or O*O?

Thanks a lot for the reply. I do understand the definition of Euler angles. I feel like the way I put my question was not very clear so let me rephrase it: what happens when we rotate the body itself with its attached XYZ axes about the space-fixed-z axis? For example in the above figure...

I hope someone can explain this to me. In the definition of Euler angles, the body-fixed-azimuthal angel γ is measured from the nodal line that defines the intersection of the body-fixed-XY plane and the space fixed-xy plane to the body-fixed-Y axis. This is the green line in this image from...

Oops! Then I am moving my question to general math

I assume the general form of the potential is 1/2 m w^2 (r-r0)^2

The spherical oscillator problem is for a potential centered at the origin.. but what if the particle is confined to oscillate at a small shift by a small (not infinite) barrier? The potential is now centered about the new position.. Could someone please suggest a way to solve the problem for...

The well known Euler angles (αβγ) are defined as in the image It is easy to see that under inversion α → π+α β → π-β but I cannot figure out how γ transforms under inversion. actually I am stuck at the question whether I should measure it from the same intersection line ON (thence γ →π+γ) or...

Thank you DrDu

Does it mean that when the crystal lacks any symmetry at all, i.e. when it is classified as C1, all terms in the expansion are important?

I find in many textbooks that when expanding the crystal field in spherical harmonics, those terms of odd ranks do not appear in the expansion even if the crystal lacks an inversion centre such as the tetrahedral crystal field. Why is that? and when one should include spherical harmonics of odd...

My experience with data fitting is poor so I am in real need for help. The potential in the following is periodic over [0,Pi] I need to find a fitting function that I can use to perform further mathematics. Fourier series does not work, but a 40-degree polynomial give the following fit...

I want to simulate STM images of some compound composed of 3 molecules A, B and C.. Which is the right way to do the simulations? *Use the known equilibrium geometries of A, B and C as input for simulating the compound? or *First optimize the geometries of A, B and C independently and then use...