5:38 AM
@JohnRennie hi sir

@satan29 hi :-)

sir, how does current flow work in the quantum picture?

@satan29 you mean current flowing in a conductor?

yes

The electrons in the conduction band of a conductor behave almost like free particles. Inside the metal they can move freely and the only restriction is when they hit the edge of the wire.
So the wavefunctions of the individual electrons are like momentum eigenstates i.e. each electron behaves as a wave with a certain momentum. OK so far?

5:45 AM
ok
@JohnRennie is momentum something better associated with a particle...

The free particle solutions $e^{i(kx-\omega t)}$ are momentum eigenstates. The momentum is $\hbar \mathbf k$.

ok

Which makes sense. A free particle will move at constant speed in a straight line i.e. it has a constant and well defined momentum. So you'd expect it to be a momentum eigenstate.
(as well as an eigenstate of the Hamiltonian)

@JohnRennie sir its coming out to be $-\hbar k$

$\hat p = -i\hbar\frac{d}{dx}$
$$\frac{d}{dx} e^{i(kx-\omega t)} = ik e^{i(kx-\omega t)}$$

5:51 AM
carry on, sorry

:-)
The physical interpretation of this is that if you look at the electrons in the conduction band of a metal they are all whizzing around at different speeds (i.e. different momenta) like the molecules in a gas, but because the velocities are symmetrically distributed the net motion averaged over the electrons is zero.
i.e. on average no current flows. OK so far?

ok so far

When you apply an electric field this changes the eigenstates because now the Hamiltonian has a potential energy term from the field.

ah

The eigenstates are still approximately momentum eigenstates, but their energy gets shifted. The momentum states that travel in the opposite direction to the field have their energy lowered while the states that travel in the same direction of the field have their energy raised.

5:56 AM
why are they still momentum eigenstates?

So what happens now is that the electrons have a net momentum i.e. when you add up the total momentum of all the electrons in all the states you find there is a net momentum in the opposite direction to the field.
@satan29 I don't remember the details, just the basic principles.

ok

The point is that now there is a net momentum i.e. a net motion of the electrons, and that is just what we call a current.

got it
sor can QM reproduce the maxwells equations entirely?

That's a complicated question ...
QM cannot reproduce Maxwell's equations. Do do that we need quantum field theory i.e. quantum electrodynamics.

6:04 AM
hmm

But for that we start with the vector four-potential from Maxwell's equations and quantise it. So QED reproduces Maxwell's equations because it starts from Maxwell's equations.

oh, bummer :/

Or I guess it's fairer to say that both QED and Maxwell's equations are derived from the same Lagrangian.
A classical treatment of the Lagrangian gives ME and a quantum treatment gives QED.

@JohnRennie wait, so in a sense the maxwells equations are more fundamental than QFT !?

See above. Both derive from the same Lagrangian.

6:07 AM

You probably need to ask in the hbar. You're now pushing at the limits of my knowledge of QM :-)

:-)

I need to work for a bit. I'll be back in about an hour.

5 hours later…
11:04 AM
@JohnRennie hi sir

@satan29 hi :-)

sir are you here till 5 pm?
i.e 30 mins more

Yes ...

can I share a google doc

Yes

11:05 AM
sir just keep it for now, Ill need it tomorrow

sir can you explain the para "power spikes"

Motors also act as generators. When you first apply an EMF to a motor it draws a large current, then as the motor starts rotating it generates a back EMF that opposes the applied EMF. If you had a perfect motor (no friction) then the motor would speed up until the EMF it generated was equal to the applied EMF and at this point it would run at constant speed drawing no current.

hmm
yes, that meks sense

A real motor has friction, so it accelerates until the difference between the applied EMF and generated EMF decreases to the level needed to overcome the frictional losses.

11:11 AM
right

Anyhow, if you suddenly remove the applied EMF then the back EMF is unopposed and will be trying to pump a reverse current back through your PSU.

PSU?

Power Supply Unit

Ah

And if you reverse the EMF then you'll get an extra large current

11:12 AM
hmm

Because now the motor acting as a generator and the reversed EMF are both pushing a current back through the PSU in the reverse direction.

that makes sense
what was x-x eariler is now x+x

Yes. So you'll get a transient extra large current.

got it.

The current decreases as the motor's rotation slows to a halt then reverses.

11:18 AM
sir do you kniw what a servo motor is>

Vaguely ...

from my experience, your "vaguely" is good enough :-)

A normal motor just spins, and it spins faster the more voltage you apply.

yes

A servo motor is design to rotate by some specified angle then stop.

11:20 AM
oh

They are used for controlling machinery e.g. in a remote control vehicle you could use a servomotor to control the steering.

hmm

i.e. you can get it to turn the steering wheel by x degrees where x is any value you want.
There is a very similar type of motor called a stepper motor

ok

This works by rotating in fixed steps, and you determine the angle by how many steps you make the motor move.
However you are limited to a resolution of one step i.e. you can't turn the motor by half a step.

11:23 AM
right

A servo motor moves smoothly an the resolution is only limited by the sensitivity of the mechanism you used to build the motor.
I don't know a vast amount about this. I have used these types of motors for building RC stuff, but that was decades ago.
I imagine the technology has moved on since then :-)

sir final question
I know the physics behind gyroscope and gyroscopic precession

Yes ... ?

but
Gyroscope: A gyroscope is a device used for measuring or maintaining orientation and angular velocity.[1][2] It is a spinning wheel or disc in which the axis of rotation is free to assume any orientation by itself. When rotating, the orientation of this axis is unaffected by tilting or rotation of the mounting, according to the conservation of angular momentum.
I dont understand how it used practically?

I guess it depends what you are using the gyroscope for. Are you thinking of its use in navigation systems?

11:30 AM
yes

In a navigation system you need to know what direction you are moving in. A compass gives you some idea but it isn't so good for measuring the up and down directions, and it can be used at all in some circumstances e.g. on a fighter plane that is screened against EM.
So you use a gyroscope mounted inside a gimbal that allows near frictionless motion about any axis.

@JohnRennie EM?

An electromagnetic pulse (EMP), also sometimes called a transient electromagnetic disturbance, is a short burst of electromagnetic energy. Such a pulse's origin may be a natural occurrence or human-made and can occur as a radiated, electric, or magnetic field or a conducted electric current, depending on the source. EMP interference is generally disruptive or damaging to electronic equipment, and at higher energy levels a powerful EMP event such as a lightning strike can damage physical objects such as buildings and aircraft structures. The management of EMP effects is an important branch o...

ok
@JohnRennie alright, but how does it detect directin?

If your superfighter can be knocked offline by an EM pulse you're not going to survive very long :-)

11:33 AM
yes XD

@satan29 Once you spin up the gyroscope it will always point in the same direction i.e. its angular momentum vector remains constant.

and that helps how?

So you just have a sensor that measures the direction of the plane relative to the direction of the gyroscope. Then you have an absolute measurement of the direction the plane is going.

ohh

You need to read more science fiction. If you did you'd know all this stuff. I've long thought the educational system doesn't place enough emphasis on reading science fiction :-)

11:37 AM
:-)
thanks for today sir.

Admittedly you'd also believe that transdimensional warp drives exist ...
I was devastated when I learned GR and discovered that they didn't.

well yes, Ill be trubling you with an entirely different set of qns

OK. I'm off now to score some lunch.

DoEs A wOrMhOlE ReaLlY ExIsT?

Absolutely!!!
(* not)

11:39 AM
XD