Quantum half-integer

The integer n labels the wavefunctions and is called a quantum number. In general, a quantum number is an integer (or, in some cases, Section 1.10, a half-integer) that labels a wavefunction, specifies a state, and can be used to calculate the value of a property of the system. For example, we can use n to find an expression for the energy corresponding to each wavefunction. 

This inequality of interactions leads to a phenomenon whose quantum-mechanical nature will be addressed later (Chapter 7), and whose practical appearance is given here simply by description. Let us first make the distinction between half-integer... 

Finally, we can demonstrate that the degeneracy is even when the total angular momentum quantum number F is half-integer, again via a reductio ad absurdum method. Suppose that the degeneracy of the eigenstates is k, then we... 

A spinning electron also has a spin quantum number that is expressed as 1/2 in units of ti. However, that quantum number does not arise from the solution of a differential equation in Schrodinger s solution of the hydrogen atom problem. It arises because, like other fundamental particles, the electron has an intrinsic spin that is half integer in units of ti, the quantum of angular momentum. As a result, four quantum numbers are required to completely specify the state of the electron in an atom. The Pauli Exclusion Principle states that no two electrons in the same atom can have identical sets of four quantum numbers. We will illustrate this principle later. 

Goldbourt, A. and Madhu, P.K. (2005) Multiple-quantum magic-angle spinning high-resolution NMR spectroscopy of half-integer spin quadrupolar nuclei. Annu. Rep. NMR Spectrosc., 54, 81-153. 

Fig. 23. Effect of static ZFS on the NMRD profiles for integer (S = 1) electron spin quantum numbers (panels A, C, and E) and half-integer (S = 3/2) electron spin quantum numbers (panels B, D, and F). Conditions Aj = 0.1 cm, = 5 x 10 s (A) and...

QUANTUM NUMBER. A number assigned to one of the various quantities that describe a particle or state. Many different characteristics of atomic and nuclear systems, as well as of those entities that arc introduced as a part of particle physics, are described by means of quantum numbers. The quantum numbers arise from the mathematics of the eigenvalue problem and may be related to the number of nodes in the eigenfunction. Any state may be described by giving a sufficient set of compatible quantum numbers, In the customary formulations, each quantum number is either an integer (which may be positive, negative, or zero) or an odd half-integer. 

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