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Oct
13
comment Should the eigenkets be weighted in $|P\rangle = \sum\limits_{r}|\xi^r\rangle$?
every ket-vector can be expressed as a sum of a set of unity weighted eigenvectors? I find this hard to believe.
Oct
5
comment Why does Dirac write $\langle\xi'|\overline{f(\xi)} = \overline f(\xi ')\langle\xi'|$?
@KyleKanos Why doesn't Dirac just substitute $\xi'$ into $\overline{f(\xi)}$ as for (34)?
Oct
5
comment Why does Dirac write $\langle\xi'|\overline{f(\xi)} = \overline f(\xi ')\langle\xi'|$?
@KyleKanos Dirac uses $\xi$ for a real linear operator, ' to label objects connected with eigenvalues-- $\xi'$ for an eigenvalue, $\langle\xi'|$ for an eigenbra
Sep
23
comment How does Dirac form this conjugate imaginary equation?
@ACuriousMind This is page 30 of his book where the basic mathematical framework is based around there being a function of a ket, amongst other things. You really need to have a look at the book to see what I mean.
Sep
20
comment What axiomatizations exist for special relativity?
Nowadays, we'd say there is a universal speed limit c that light happens to travel at, making its measurement convenient.
Sep
18
comment How can (in Dirac's terminology) the product of two “real” linear operators be “not real”?
This answers my question. It would help if you could put $\alpha = \bar\alpha$ in brackets after Hermitian.
Sep
3
comment How does Dirac show that $\langle B|\bar{\bar{\alpha}}|P\rangle\;=\; \overline{\langle P|{\bar{\alpha}}|B\rangle}\;=\; \langle B|{\alpha}|P\rangle$?
Indeed; I assumed that the adjoint of an adjoint cancelled like the inverse operator. It seems obvious now that the adjoint of an adjoint should initially be assumed to give a different linear operator since its still just a linear operator.
Aug
25
comment Explanation for $E~$ not falling off at $1/r^2$ for infinite line and sheet charges?
@RonMaimon now that you've had a long rest, does this answer still make sense to you honestly?
Aug
24
comment Is there a “forwards” and “backwards” in one dimension?
So a magnitude can be negative?
Aug
24
comment Is there a “forwards” and “backwards” in one dimension?
@HDE226868 sure you can. But maybe that isn't a true one dimensional space as defined by a physicist or mathematician, and a direction paramaterized by two discrete symbols +,- has been added.
Aug
24
comment Physical reason for Lorentz Transformation
You're only looking at a light-like interval; you need to show how invariance of this implies invariance of space-like and time-like intervals also.
Aug
20
comment Rotation axis of a rigid body
+1 all this work, and just one lousy up-vote?
Aug
19
comment Why should multiplication of a ket vector by a complex number change only its “direction”?
@ACuriousMind A vector multiplied by a negative real number changes its direction, yes? How are we to interpret multiplying it by a complex number?
Aug
19
comment Why should multiplication of a ket vector by a complex number change only its “direction”?
@Nathan I'm looking for an answer in the spirit of Dirac talking vaguely about vectors in an infinite dimensional space up to this point. I guess this will become clearer later on in the book, but Dirac seems to suggest this statement is obvious for physical/mathematical reasons.
Aug
19
comment When is it useful to distinguish between vectors and pseudovectors in experimental & theoretical physics?
Cool, is there a book you can recommend which goes into this in more detail?
Jul
23
comment What is a tensor?
A tensor is a geometrical object whose components transform like that of a tensor.
Jul
11
comment How does the speed of electrons change around a circuit?
The drift velocity is typically around a few centimeters/hour.
Jun
13
comment Why Lorentz Transformation in Special Relativity has to be like this?
You've thought about this before, right?
May
2
comment What transformation is the metric of general relativity invariant under?
@Siva Tullio Levi-Civita does both in his original book. I get the feeling that physicists skimmed over it, and just took out the bit defining a tensor as having components transforming in a certain way.
Apr
11
comment Invariance of Lagrange on addition of total time derivative of a function of coordiantes and time
There isn't an absolute path in Galilean mechanics, the paths ARE different in the two frames where $x' = x -Vt$