Recent content by ExplosivePete

Good point. There are a lot of nice tricks that would be nice to see summarized somewhere as far as techniques for choosing the ansatz. It is also useful to look at when the particle is in a "classically restricted region" (E < V(x)). In these regions, the wave function will be concave down (as...

In a typical quantum course we learn how to approximate the ground state of a particular Hamiltonian by making an educated guess at an ansatz with a tunable parameter then calculating the expectation energy for the ansatz. The result will depend on the tunable parameter if done correctly. Then...

Hello, Could someone help me find a general derivation of the formula for addition of capacitance of conductors? I'm hoping to find something that could be applied to a general assortment of conductors, not just parallel plate capacitors. I look forward to your response, Pete

Thanks for your reply. I am apply to programs all over the US. I take your point that research funding is very fluid and subject to change, that is a good thing to be aware of. I recognize that a reply to this question is subjective, but I think hearing those opinions is important and useful to...

I am applying to phd programs in physics right now. I am interested in doing research in quantum information science. I see there is a lot of interest and funding for quantum information science right now, but does anyone have any advice on whether or not this research will be well funded in the...

I hope you have found your solution 5 years later, but since others may have the same question and because I find the theorem very interesting and possibly useful, I'll post. The Gershgorin disk theorem gives us that the spectrum of the matrix is a subset of the union of the gershgorin disks...

Griffiths introduction to electrodynamics talks about how electric potential is always continuous and electric fields are continuous except in the case of a surface charge density. This seems fair assuming you can have a continuous surface charge Density, but in the real world, these densities...

I am in a quantum mechanics course based on the Griffiths text. When the books talks about the wave function on an electron in a specific state, it refers to the "complete state" of the electron as being the product of the spatial part and the spin part of the wave function. The need to...

When we solve for solutions to differential equations, in physics we are often only interested in nontrivial solutions. I'm not certain of this, but it is my intuition that the space containing the solutions contain some form of a zero element. Physically, we are uninterested in these trivial...

Please review my post again. Hopefully it is both more legible and up to PF guidelines.

1. ... Expand the Eigenvalue as a power series in epsilon, up to second order: λ=[3+√(1+4 ε^2)]V0 / 2 Homework Equations I am familiar with power series, but I don't know how to expand this as one.[/B]The Attempt at a Solution :[/B] I have played around with the idea of using known power...

I appreciate all the feed back.

Hello. Next fall I shall be applying to graduate programs in the fall. I will be graduating with undergrad degrees in both physics and math. This has made it difficult for me to figure out where to go from here. I am hoping to get some insight of what research fields would be a good fit for me...