Dear Members,

In Sakurai's Modern Quantum Mechanics, what is the Coefficient
"epsilon" in commutation relation (1.4.20)?

cheers,
Ali

"Ali" wrote in message
oups.com...
Dear Members,

In Sakurai's Modern Quantum Mechanics, what is the Coefficient
"epsilon" in commutation relation (1.4.20)?

cheers,
Ali

It's an abbreviated notation for the completely antisymmetric tensor
with three indices. It equals 0 if two indices (axis labels 1,2,3) are
equal, +1 if they are an even permutation of 123, -1if an odd
permutation of 123. See Messiah II, p. 510 or most any book on tensors.

John Lowry
Flight Physics

On 2005-06-01, Ali wrote:
Dear Members,

In Sakurai's Modern Quantum Mechanics, what is the Coefficient
"epsilon" in commutation relation (1.4.20)?

Sakurai is a common book, but it would also not hurt to briefly
reproduce the equation and some of the context in your post.

The equation in question is

[S_i,S_j] = i eps_{ijk} hbar S_k.

These are standard commutation relations for spin operators. The symbol
eps_{ijk} is the Levi-Civita tensor. It is zero whenever any of the ijk
indices are repeated. It is 1 when ijk=123 or any even permutation
thereof. It is -1 when ijk is any odd permutation of 123.

Sakurai assumes the reader is at an advanced undergraduate or beginning
graduate level in a physics or related program. It is a good book, but
you may want to consider starting with a more elementary one, for
example _Introduction to Quantum Mechanics_ by Griffiths. Another book
is _Introductory Quantum Mechanics_ by Liboff. If you are doing self
study, _Schaum's Outline of Quantum Mechanics_ has lots of worked
problems.

Igor