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[guitar_hero]

Hallo! This is me. Call me, beep me, if you wanna reach me. Or, you know, just leave a message

voice/text/action

Comments

ACTION / March 17th ||

[guitar_hero]

[well, this is comfortable. he doesn't mind it a bit. He settles himself and smiles a bit at her request.]

You asked for it. [he clears his throat]

The form of the Schrödinger equation depends on the physical situation (see below for special cases). The most general form is the time-dependent Schrödinger equation (TDSE), which gives a description of a system evolving with time

A wave function that satisfies the nonrelativistic Schrödinger equation with V = 0. In other words, this corresponds to a particle traveling freely through empty space. The real part of the wave function is plotted here.

Show it on blackboard between doodles of the system of Cazmatoz and maybe Peter Rabbit just to see if they're paying attention.

And then tel them that... Each of these three rows is a wave function which satisfies the time-dependent Schrödinger equation for a harmonic oscillator. The top two rows are examples of stationary states, which correspond to standing waves. The bottom row is an example of a state which is not a stationary state. The right column illustrates why stationary states are called "stationary".

Such as the nonrelativistic Schrödinger equation for a single particle moving in an electric field, but not magnetic.

If you look at the time-dependent Schrödinger equation in position basis blah blah add other fomula

where μ is the particle's "reduced mass", V is its potential energy, ∇2 is the Laplacian (a differential operator), and Ψ is the wave function (more precisely, in this context, it is called the "position-space wave function"). In plain language, it means "total energy equals kinetic energy plus potential energy", but the terms take unfamiliar forms for reasons explained below.

Given the particular differential operators involved, this is a linear partial differential equation. It is also a diffusion equation, but unlike the heat equation, this one is also a wave equation given the imaginary unit present in the transient term.

In essence the term "Schrödinger equation" can refer to both the general equation, or the specific nonrelativistic version. The general equation is indeed quite general, used throughout quantum mechanics, for everything from the Dirac equation to quantum field theory, by plugging in diverse expressions for the Hamiltonian. The specific nonrelativistic version is a strictly classical approximation to reality and yields accurate results in many situations, but only to a certain extent.

[a pause]

Understand?

ACTION / March 17th ||

[bigbadrose]

[She fell asleep from the moment he started talking about Schrdoinger. So... good luck with that.]

Mm-hm. [Those are sleep mumbles in response to a completely different question of being asked whether she was good and comfy because they're on a nice sandy beach with coconut drinks and he's laughing and asking if she's happy now.]

ACTION / March 17th ||

[guitar_hero]

Well it's rubbish. Memorized it off Wikipedia. Oh the theory is sound for the time and place but it couldn't explain its way out of a paper bag.

[he considers his notes while absently stroking her hair]

Re: ACTION / March 17th ||

[bigbadrose]

[That startles her out of sleep enough to blink open.] Whot, really???

[On can never tell with the Doctor. Doctors are tricksy.]

ACTION / March 17th ||

[guitar_hero]

Wot really wot? [he's amused] That surprises you?

Re: ACTION / March 17th ||

[bigbadrose]

Of course!

Can't you get kicked out for using Wikipedia? Or does that not apply to teachers, only students? You're setting a terrible example, Teach!

[Unless she dreamed that.]

ACTION / March 17th ||

[guitar_hero]

didn't say I was going to use it. Just that I'd memorized it and it's rubbish. [he tugs at a strand of her hair] Go back to sleep.

Re: ACTION / March 17th ||

[bigbadrose]

Nuh-uh! I wasn't sleeping! [She totally was!] I was listening. All about Schrodinger's stationary waves, which means they were oscillating. Like how swimshorts and ocean waves don't. Which is a shame.

[Rose is very not picturing the Doctor in shrodinger swimshorts with stationary waves that may or may not be there given any portion of a mai tai.]

Basically electrons existing in the fifth dimension, are they there? No, they're in a field, because trying to find where they are changes them. Like me and my cannon.

[BACK ASLEEP ALREADY.]

ACTION / March 17th ||

[guitar_hero]

[he can't help but be a little impressed and slightly turned on. But she is back asleep before he can get a chance to tell her so. So he just chuckles and strokes her hair, enjoying the peace of the moment. It's a beautiful night...]