Chronology |
Current Month |
Current Thread |
Current Date |

[Year List] [Month List (current year)] | [Date Index] [Thread Index] | [Thread Prev] [Thread Next] | [Date Prev] [Date Next] |

*From*: Diego Saravia <dsa@unsa.edu.ar>*Date*: Thu, 6 Dec 2018 16:02:40 -0300

thanks!!!!

El mié., 5 dic. 2018 a las 20:43, John Denker via Phys-l (<

phys-l@mail.phys-l.org>) escribió:

On 12/5/18 4:04 PM, Diego Saravia wrote:

Is there a general demostration along these lines about area in clasicalhttps://physics.stackexchange.com/questions/63318/phase-space-in-quantum-mechanics-and-heisenberg-uncertainty-principle

phase space and dimension of quantum states (number of base states) or a

published one?

Pretty much any book on statistical mechanics touches on

this. They tend to not spend much time on it. Sometimes

they just assume it in passing rather than explaining it.

Often they assume you know things like:

-- The classical Liouville theorem says area in phase space

is conserved. There are lots of accessible writeups on

this.

-- The corresponding QM result says that the equations

of motion are unitary, and therefore area in phase space

is conserved.

-- There is a concept of "state" i.e. microstate. To do

thermodynamics you need to be able to enumerate a set of

basis states. There's an influential book by some guy

named Boltzmann (1898) that really pounds on this idea.

However, I wouldn't call this "accessible" ... I find

it nearly impenetrable. But lots of good stuff is there

if you know what to look for.

-- In cases where it is easy to enumerate the quantum

states, e.g. harmonic oscillator or particle in a box,

it is easy to show that the area per basis state is h

(not hbar). Unitary evolution means that any other

basis will have the same property. There's an influential

published paper by some guy named Planck (1903) that

makes this point.

When Boltzmann's book came out, Planck was one of the

few guys smart enough to read it and make sense of it.

And wow, he really made good use of it.

Possibly useful:

https://ocw.mit.edu/courses/nuclear-engineering/22-02-introduction-to-applied-nuclear-physics-spring-2012/lecture-notes/MIT22_02S12_lec_ch6.pdf

Also Feynman's _Statistical Mechanics_ book talks about

the fundamentals. The ideas are correct and well explained,

but it was not carefully edited, so beware of typos in the

formulas.

Feynman and Hibbs _Quantum Mechanics and Path Integrals_

will change the way you think about everything (including

thermodynamics) but it is not an easy read.

_______________________________________________

Forum for Physics Educators

Phys-l@mail.phys-l.org

http://www.phys-l.org/mailman/listinfo/phys-l

--

Diego Saravia

dsa@ututo.org

Diego.Saravia@gmail.com

NO SIEMPRE FUNCIONA->dsa@unsa.edu.ar

**References**:**Re: [Phys-L] uncertainty principle .... was: ground-state energies***From:*Diego Saravia <dsa@unsa.edu.ar>

**Re: [Phys-L] uncertainty principle .... was: ground-state energies***From:*John Denker <jsd@av8n.com>

- Prev by Date:
**Re: [Phys-L] uncertainty principle .... was: ground-state energies** - Next by Date:
**[Phys-L] The state of govt. science** - Previous by thread:
**Re: [Phys-L] uncertainty principle .... was: ground-state energies** - Next by thread:
**[Phys-L] The state of govt. science** - Index(es):