In non-rotating stars, modes with the same angular degree must all have the same frequency because there is no preferred axis.
2.
The above conventions imply a preferred axis ( for example, the " z " direction in Cartesian coordinates ), and they also imply a preferred direction along this preferred axis.
3.
The above conventions imply a preferred axis ( for example, the " z " direction in Cartesian coordinates ), and they also imply a preferred direction along this preferred axis.
4.
In modern quantum mechanics, the angular momentum is quantized the same way, but the discrete states of definite angular momentum in any one orientation are quantum superpositions of the states in other orientations, so that the process of quantization does not pick out a preferred axis.
5.
Taking into account the quantization of the angular momentum vector is immaterial : an orbital of given " ! " and " m " & prime; obtained for another preferred axis " z " & prime; can always be represented as a suitable superposition of the various states of different " m " ( but same " l " ) that have been obtained for " z ".
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