Recent content by tommyli

Hey people, I need to calculate inner product of two Harmonic oscillator eigenstates with different mass. Does anybody know where I could find a formula for \int{ H_n(x) H_m(\alpha x) dx} where H_n, H_m are Hermite polynomials?

Replace i in Euler's formula with i -1 and you get a logarithmic spiral: e^{(i - 1)t} parametrically describes a logarithmic spiral in the complex plane

If force is a derivative of some function of spatial coordinates, this function is called the potential energy, and the force is conservative. Non-conservative forces are certainly not derivatives of any function.

Whenever you write df it implies that the differential operator is applied to the function f, so if you write work as an exact differentail dW implicitly you are saying force can be written as the derivative of some function of spatial coordinates.

It is only an exact differential int he case of a conservative force. Precisely, if there is a potential we write dU = -Fdr which implies that F = -dU/dr.

Hi jsgruszynski, Thankyou for your quick reply. For AC voltage I understand; however even when there is no voltage applied, you should be able to detect thermal fluctuations in a voltmeter (?) If I integrate the signal in time-domain over a "box" of size 1 millisecond, the effective bandwidth...

Hello, I was wondering if anybody could answer a quick question: What is the typical level of Johnson-Nyquist noise in an analog voltmeter in equilibrium (short circuited)? Is it millivolts? What is the level for an AC current of order mA at 50Hz?

What you are saying about virtual photons is true only for interacting fermions which are asymptotically free. For example, if you have an electron moving through a homogeneous electric field, the electric force is the charge multiplied by the electric field; it has nothing to do with virtual...

Hi gespex, Yes, what you are saying is true, although in physics we usually do not talk about magnetic poles, instead we talk about magnetic moments and the interaction between magnetic moments. A monopole (magnetic pole) is a single point containing magnetic "charge" from which magnetic flux...

The electroweak interaction has a gauge group U(1) x SU(2). Within this gauge group you must be able to find the gauge group of electromagnetism, which is U(1). Electromagnetism cannot simply correspond to the U(1) subgroup in the product, it so happens that it corresponds to the subgroup of...

Hi Bob, I think this is a very fair question. I've also heard of things like this from TV documentaries on string theory. I think those who have already commented are much more qualified to talk about this since it is something I know very little about, but I think I can offer a simple...

The simple answer is that local U(1) symmetry gives rise to conservation of charge by Noether's theorem, yes. But you have to be careful.. the U(1) occurring in the standard model is not electric charge but weak charge which is a combination of electric charge and isospin. The operator of...

Ok I understand your point. You are saying that if you have non-overlapping wavefunctions then there is effectively no difference between writing the separable wavefunction or the antisymmetric product, but to be consistent you must choose the antisymmetric product for the interacting and...

Hi Ken, It's an entirely semantic issue. On the level of formal field theory I absolutely agree with you, in a system of interacting particles there is no experiment that can distinguish particles. As long as you have one of those particles leaving the system and traveling to the other side...

Hi Ken, thankyou for your comments. In my response i cared very little about formal field theory, i always think its better to start from a simple physical situation to elucidate a question like this. There is no need to go into formal details for this kind of question, when you think about...