Recent content by StatMechGuy

A minimum uncertainty state that's also the eigenstate of an hamiltonian is a gaussian, and it corresponds to the harmonic oscillator hamiltonian.

Perturbations can both increase or decrease the total energy of the system. Just look at first order corrections: \Delta E^{(1)}_n = \langle n|V|n\rangle Why would you assume that this matrix element has to be positive? Also, your perturbative expansion is really a Taylor expansion in...

Not evaluating the integral. Just compute it and see. Then, calculate <p^2> and take its root mean square and tell the kid that.

Multiply the left hand side by the energy denominator. Insert the hamiltonian operator. The commutator trick should then work.

Never trust a math professor to teach you physics. They'll obscure a painfully obvious concept under layers of formalism just so that they can show that it does in fact work the way physicists know it works. The trick is to know when that level is needed, and when it isn't.

There's a discontinuity in the derivative of the function from the left and from the right, and the idea is to figure out that jump by looking at the delta function. Also, don't worry about the wave function being a distribution. It's still a function that satisfies a certain differential equation.

The modulus squared of the wave function is a probability distribution. Is there any physical reason to say that at the point x = 0 + \epsilon there's one probability density, and then at x = 0 - \epsilon it's wildly different? Also, the continuous first derivative rule comes from a similar...

You can reduce the problem (through conservation of energy) to what's called an elliptic integral. This leads you to a study of elliptic integrals, and their various limits, which is of some interest. Another interesting problem is the so-called "inverted pendulum" where you drive its base with...

As has been mentioned, "squeezed states" in quantum optics are an example of a minimum uncertainty state. Coherent states are a special case of squeezed state, where the uncertainty is equally distributed between the canonically conjugate coordinates. It's worth noting that this can refer to...

If the entire universe is just these two bodies, and there are no external forces whatsoever, then there are no external forces. If you transform into a reference frame with the center of mass then with no external forces it is by definition an inertial reference frame. However, this trick...

Try to come up with a coordinate transformation that does any good. Relative coordinates don't work, you need three to specify everything. This is no better than the starting position. Just give it a shot and you'll see.

I wouldn't call coherent states "pathological states". The way you would go about proving it would probably be by construction. Start by declaring a state |\alpha \rangle to be an eigenstate of the lowering operator, then expand that state in the basis of the harmonic oscillator and see what...

In the modern system of measuring units, time is determined in terms of the frequency of oscillation for a particular element of cesium, and a meter is then defined as the distance light travels in some absurdly short period of time. So technically, the meter is defined in terms of a velocity...

Basically, the argument is as follows. System A can have its microscopic configuration specified by a set of parameters A_1, A_2, etc. The same can be done for system B and system C. If A and B are in thermal equilibrium, that this indicates that there is a "constraint equation" (same concept...

You may find that the radius cancels out... Go ahead and solve the problem with arbitrary variables and then see if anything nice comes of it.