Re: Various Questions

[Samuel Held <Held@RHIP.PHYS.UTK.EDU>]

Jim,

> 1) Various texts give different results for Dx Dp: should this be h,
hbar
> or hbar/2 -- what is with this variation?????  How did Heisenberg write
it???

I have this explanation from more than one insturctor.  Dp Dx >= hbar/2
is the
proper and exact solution.  However in problems, it is OK to use just
hbar because
it is only a factor of 2 off (like the Fermi estimations).  I have never
seen h
used because then you off by a factor of 4pi which gets you in more
trouble.

> 2)  For the First Law, what symbol is preferred these days for DQ and
DW:
> Delta, delta, dbar, or some other Byzantine symbol?

The dbar is for an inexact differential or one that has path and history
dependences.
The d is an exact differential (path and history independent - what we
see in calculus
class.
The small delta is for infinitsimal changes in the variable more like
quantum (atomic) size.
The big Delta is for large (classical - macroscopic) changes.
That is what I have been taught and seen in the textbooks I have used.
It also varies on the author's background and training.

> 3) How would one refer to the two parts of DxDp phase space?  Real?
> Momentum?  Momentum is just as real as Dx isn't it?  Any suggestions
for
> customary usage?

Momentum space is just as real as coordinate space.  We just use p_x,
p_y, and p_z as the axes.  It is like frequency space in a Fourier
transform in that the problem may be more easily solved in momentum
space and then transformed back into coordinate space.  We need this
since we perceive things in coordinate space and our intuition lies
there.  I hope that answers the question you are asking, because like
David I am little confused over the exact question you are asking.



Sam Held