Recent content by Christopher Grayce

Why not? Your exponential factor is just a number, and it commutes with every operator inside the parentheses.

Start with this book: https://www.amazon.com/dp/0123870321/?tag=pfamazon01-20 But I would say the history of theories using only 2-body correlations for liquids is not great. Sometimes things work, sometimes they don't, and I don't think people have had much success predicting ahead of time...

That's why I gave you Levine. The people who study the quantum mechanics of molecules are chemists, and a rigorous book on physical chemistry is where you'll find the most careful explanation of the BO approximation.

The reaction you want is 4 HNO3(aq) -> 4 NO2(aq) + O2(g) + 2 H2O(l). You can probably calculate a decent heat of decomposition using the heats of formation of the compounds involved.

It does seem like a strange example. In general for most simple substances dG = ‒SdT + Vdp + μ dN, so there *are* no processes that can change G of a simple substance at constant T and p, except for the trivial one of adding or subtracting some of the substance (dN != 0). So their example...

Probably Levine, "Quantum Chemistry," has what you're after. A classic textbook.

They are comparing the number of microstates of the universe at its beginning with the number now, which is much, much greater. Perhaps you are confused because you are imagining that the correct number of microstates to count then was the number (if any) that the universe could also have been...

What you do know, from general thermodynamic principles, is that A and B must be intensive parameters (e.g. T or P for the simplest of systems). Which they are depends on what kind of equilibrium you have established. If you only allow A and B to exchange energy, then, yes, at equilibrium the...

DC motors use a commutator and brushes to reverse the current through the armature every half turn, so the magnetic field does indeed change (grow and shrink) as it does in an AC motor, and of course that requires energy, so even if the *DC* (zero frequency) resistance of the armature is zero...

The way electromagnetic waves carry data is by altering the base wave. So, you can bump the amplitude of the wave a bit, or the frequency, or the phase, and so forth. Every time you do that, though, you are causing the original wave to occupy a finite band of frequencies instead of just one...

That's correct, the astronauts (and ISS itself) do not exert a force on the Earth other than their own gravitational pull, but you might want to bear in mind that the force of gravity is the *product* of the two masses, so the force between the astronauts and the Earth is quite significant, as...

Magnetic fields only affect the motion of particles with an electric charge, or an electric or magnetic dipole (quadrupole, et cetera) moment. So, protons, yes, electrons, yes, even neutrons weakly (because while they have no electric charge they do have a magnetic dipole moment), but not...

How do you know you've changed the spin if you don't know its original value?

In what form do you know the definitions of the dot and cross product of two vectors? If you know them in terms of the angle between the vectors, use that. If you know them only in terms of multiplication of the components (e.g. A.B = AxBx + AyBy + AzBz) then you can draw some triangles and...

Expand the t=0 wavefunction (presumably the g.s. of a particle in a box) in free particle plane waves with positive momentum and having a node at the left wall.