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I read this quote from an article and another like is is

http://scienceblogs.com/principles/2010/07/electron_spin_for_toddlers.php [Broken]

"and we see that the half-angle appears with a rather interesting consequence. To see this consequence let’s consider a rotation of 360 degrees – 2 radians. Substituting yields

|a>

In other words, upon a rotation of 2 pi the state ket does not return to it’s original state – there is an additional factor of a minus. In order to get back to the original state ket one must rotate through 720 degrees. This is the origin of the statement that an electron is unsual in the fact that when rotated through a full circle it does not “look the same”. "

Now I thought that |a> and -|a> represented the SAME state because -1 is just exp i(pi) which has square modulus of 1. According to the postulates of QM this should represent the same state?

Can anyone put me into the right way of thinking here?

http://scienceblogs.com/principles/2010/07/electron_spin_for_toddlers.php [Broken]

"and we see that the half-angle appears with a rather interesting consequence. To see this consequence let’s consider a rotation of 360 degrees – 2 radians. Substituting yields

|a>

_{2pi}= -|a>In other words, upon a rotation of 2 pi the state ket does not return to it’s original state – there is an additional factor of a minus. In order to get back to the original state ket one must rotate through 720 degrees. This is the origin of the statement that an electron is unsual in the fact that when rotated through a full circle it does not “look the same”. "

Now I thought that |a> and -|a> represented the SAME state because -1 is just exp i(pi) which has square modulus of 1. According to the postulates of QM this should represent the same state?

Can anyone put me into the right way of thinking here?

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