Recent content by DrClaude

Edit: uploaded image doesn't look good. Try this link.

Only posts in English are allowed :smile: But yes, "physicist," not "physician."

Yes, according to the scenario as presented up to this point. On which Feynman then reflects:

Then there is no heat going to the paddel side. ε of heat is added to the ratchet side.

:welcome:

Which case are you considering: the ratchet going forwards or backwards?

https://en.wikipedia.org/wiki/Spherical_coordinate_system#Integration_and_differentiation_in_spherical_coordinates

##\ket{\psi(x)}## doesn't make sense. ##\ket{\psi}## is an (abstract) vector in Hilbert space, so it doesn't make sense to write it as having a position dependence. To convert to a wave function, you have $$ \psi(x) = \braket{x | \psi} $$ If you have, for example, a particle on a ring, "all...

I don't get it :cry: Edit: I get it now. But I'll leave the crying emoji because onions...

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You are assuming that oxygen makes up 21% of a gas of uniform molecular mass 32 amu. You have to account for the fact that nitrogen is lighter.

Correct. It will be useful to remember that ##\braket{|}## correspond to complex numbers and can be moved around equations as needed.

##|ψ'\rangle=|h2\rangle\langle h2|ψ\rangle## is nothing but ##|ψ'\rangle= c |h2\rangle## with ##c## some complex number. Physical states are defined up to an arbitrary complex scalar constant, so it is the same state.

My guess is that you have to work in both ##\theta## and ##\phi##, and integrate with the proper integration element, ##\sin \theta \, d\theta \, d \phi##.

As the masses are different, I really don't see how the energy could be the same.