- #1

anantchowdhary

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Thnx

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- Thread starter anantchowdhary
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- #1

anantchowdhary

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Thnx

- #2

jtbell

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- #3

anantchowdhary

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Sorry still haven't understood at all!

What is the quantum number?

What is the quantum number?

- #4

Crosson

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- #5

jtbell

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Sorry still haven't understood at all!

OK, let's go backwards a bit. How much do you know about angular momentum in classical mechanics? Do you know about how to represent angular momentum as a vector?

- #6

anantchowdhary

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I just about know that L=r X p

where p is linear momentum and r is the displacement position vector

where p is linear momentum and r is the displacement position vector

- #7

jtbell

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[tex]| \vec L | = L = \sqrt{l(l+1)} \hbar[/tex]

where [itex]l[/itex] is an integer 0, 1, 2, 3... Furthermore, the

[tex]L_z = m_l \hbar[/tex]

where [itex]m_l[/itex] can have values ranging from [itex]-l[/itex] to [itex]+l[/itex] in steps of 1. For example, if [itex]l = 2[/itex], then the possible values of [itex]m_l[/itex] are -2, -1, 0, +1, +2.

Something like the Earth also has

The rules for quantizing [itex]\vec S[/itex] are similar to the rules for quantizing [itex]\vec L[/itex]:

[tex]| \vec S | = S = \sqrt{s(s+1)} \hbar[/tex]

[tex]S_z = m_s \hbar[/tex]

where [itex]m_s[/itex] can have values ranging from [itex]-s[/itex] to [itex]+s[/itex] in steps of 1. The differences from orbital angular momentum are:

1. [itex]l[/itex] must be an integer, but [itex]s[/itex] can be either integer or half-integer.

2. For a particular particle (e.g. electron) [itex]l[/itex] and/or [itex]m_l[/itex] can change when its "orbit" changes, but [itex]s[/itex] is always the same for a particular kind of particle. For example, all electrons have [itex]s = 1/2[/itex], and so they must have [itex]m_s = -1/2[/itex] ("spin down") or [itex]m_s = +1/2[/itex] ("spin up").

However, [itex]m_s[/itex]

- #8

anantchowdhary

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What do you mean by quantizing [itex]\vec L[/itex] ?

The help was much appreciated.Thnx

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jtbell

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- #10

Schrodinger's Dog

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That seems fairly easy to follow, what is the difference with anti matter particles like a positron, do they spin in the opposite direction ie they go towards the other half of the circle? Or do they just spin in an opposite direction, starting at an opposite position, sorry if this is a stupid question.

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jtbell

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anantchowdhary

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and why is the spin defined in such a way?

- #13

Schrodinger's Dog

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I see, so it's just the charge that is reversed? e+ e- the spin is the same or can be the same according to an axis, thanks.

- #14

anantchowdhary

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Why is the spin defined in such a way?How do we get the equation?

- #15

Hootenanny

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Orbital angular momentum falls out when the Schrödinger Wave Equation is solved for a Hydrogen atom.Why is the spin defined in such a way?How do we get the equation?

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