The principal quantum number(主量子数)The azimuthal quantum number(角量子数)The magnetic quantum number(磁量子数) The spin projection quantum number(自旋量子数) the electron shell, or energy level. The value of ranges from 1 to "n", where "n" is the shell containing the outermost electron of that atom. For example, in cesium (Cs), the outermost valence electron is in the shell with energy level 6, so an electron in cesium can have an value from 1 to 6. the subshell (0 = s orbital, 1 = p orbital, 2 = d orbital, 3 = f orbital, etc.). The value of ranges from 0 to . This is because the first p orbital (l=1) appears in the second electron shell (n=2), the first d orbital (l=2) appears in the third shell (n=3), and so on. A quantum number beginning in 3,0,... describes an electron in the s orbital of the third electron shell of an atom. the specific orbital (or "cloud") within that subshell.* The values of range from to . The s subshell (l=0) contains only one orbital, and therefore the ml of an electron in an s subshell will always be 0. The p subshell (l=1) contains three orbitals (in some systems, depicted as three "dumbbell-shaped" clouds), so the ml of an electron in a p subshell will be -1, 0, or 1. The d subshell (l=2) contains five orbitals, with ml values of -2,-1,0,1, and 2. the spin of the electron within that orbital. since atoms and electrons are in a state of constant motion, there is no universal fixed value for ml and ms values. Therefore, the ml and ms values are defined somewhat arbitrarily. The only requirement is that the naming schematic used within a particular set of calculations or descriptions must be consistent (e.g. the orbital occupied by the first electron in a p subshell could be described as ml=-1 or ml=0, or ml=1, but the ml value of the other electron in that orbital must be the same, and the ml assigned to electrons in other orbitals must be different). The principal quantum number(主量子数) (n = 1, 2, 3, 4 ...) denotes the eigenvalue of H with the J2 part removed. This number therefore has a dependence only on the distance between the electron and the nucleus (i.e., the radial coordinate, r). The average distance increases with n, and hence quantum states with different principal quantum numbers are said to belong to different shells. The azimuthal quantum number(角量子数) (l = 0, 1 ... n�6�11) (also known as the angular quantum number or orbital quantum number) gives the orbital angular momentum through the relation . In chemistry, this quantum number is very important, since it specifies the shape of an atomic orbital and strongly influences chemical bonds and bond angles. In some contexts, l=0 is called an s orbital, l=1 a p orbital, l=2 a d orbital, and l=3 an f orbital. The magnetic quantum number(磁量子数) (ml = �6�1l, �6�1l+1 ... 0 ... l�6�11, l) yields the projection of the orbital angular momentum along a specified axis. . The spin projection quantum number(自旋量子数) (ms = �6�11/2 or +1/2), is the intrinsic angular momentum of the electron or nucleon. This is the projection of the spin s=1/2 along the specified axis. When one takes the spin-orbit interaction into consideration, the l-, m- and s-operators no longer commute with the Hamiltonian, and their eigenvalues therefore change over time. Thus another set of quantum numbers should be used. This set includesThe total angular momentum quantum number (j = 1/2,3/2 ... n�6�11/2) gives the total angular momentum through the relation .The projection of the total angular momentum along a specified axis (mj = -j,-j+1... j), which is analogous to m, and satisfies mj = ml + ms.Parity. This is the eigenvalue under reflection, and is positive (i.e. +1) for states which came from even l and negative (i.e. -1) for states which came from odd l. The former is also known as even parity and the latter as odd parityFor example, consider the following eight states, defined by their quantum numbers:n = 2, l = 1, ml = 1, ms = +1/2n = 2, l = 1, ml = 1, ms = -1/2n = 2, l = 1, ml = 0, ms = +1/2n = 2, l = 1, ml = 0, ms = -1/2n = 2, l = 1, ml = -1, ms = +1/2n = 2, l = 1, ml = -1, ms = -1/2n = 2, l = 0, ml = 0, ms = +1/2n = 2, l = 0, ml = 0, ms = -1/2The quantum states in the system can be described as linear combination of these eight states. However, in the presence of spin-orbit interaction, if one wants to describe the same system by eight states which are eigenvectors of the Hamiltonian (i.e. each represents a state which does not mix with others over time), we should consider the following eight states:j = 3/2, mj = 3/2, odd parity (coming from state (1) above)j = 3/2, mj = 1/2, odd parity (coming from states (2) and (3) above)j = 3/2, mj = -1/2, odd parity (coming from states (4) and (5) above)j = 3/2, mj = -3/2, odd parity (coming from state (6))j = 1/2, mj = 1/2, odd parity (coming from states (2) and (3) above)j = 1/2, mj = -1/2, odd parity (coming from states (4) and (5) above)j = 1/2, mj = 1/2, even parity (coming from state (7) above)j = 1/2, mj = -1/2, even parity (coming from state (8) above)