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Fund Quantum Mechanics Lect & HW Solutions 50

Fund Quantum Mechanics Lect & HW Solutions 50 - 32...

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32 CHAPTER 3. BASIC IDEAS OF QUANTUM MECHANICS n x , n y , and n z is 1, then the other two must be 0 or their sum N would still be greater than 1. That means that precisely one of n x , n y , and n z must be 1 and the other two 0. There are three possibilities for the one that is 1, n x , n y , or n z , resulting in the three different sets of quantum numbers shown in the spectrum figure 3.3. For the third energy level, N = 2, the maximum value value any one of n x , n y , and n z could possibly have is 2, but then the other two must be zero. That leads to the first three sets of quantum numbers shown in the spectrum. If the maximum value among n x , n y , and n z is not 2 but 1, then a second one must also be 1, or they would not add up to 2. So in this case you have two of them 1 and the third 0. There are three possibilities for the one that is 0, producing the last three sets of quantum numbers shown in the spectrum 3.3 at this energy level.
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