If the total angular momentum of a neutron is jn = ℓ + s and for a proton is jp = ℓ + s (where s for protons and neutrons happens to be 12 again (see note)), then the nuclear angular momentum quantum numbers I are given by: I = |jn − jp|, |jn − jp| + 1, |jn − jp| + 2., (jn + jp) − 2, (jn + jp) − 1, (jn + jp)

If we assume that the ψi form an orthonormal basis, then a maximally mixed state is a state where the λi are the uniform probability distribution, i.e. λi=1n if n is the dimension of the state. In this sense, the state is maximally mixed, because it is a mixture where all states occur with the same probability.

A “superposition” like |ψ⟩=1√2(|↑⟩+|↓⟩) is a pure state. This means that it is a completely characterised state. In other words, there is no amount of information that, added to its description, could make it “less undetermined”. Note that every pure state can be written as superposition of other pure states.

In other words, quantum states can be identified with equivalence classes of vectors of length 1 in H, where two vectors represent the same state if they differ only by a phase factor. “A quantum mechanical state is a ray in projective Hilbert space, not a vector.

four quantum numbers

The three quantum numbers (n, l, and m) that describe an orbital are integers: 0, 1, 2, 3, and so on. The principal quantum number (n) cannot be zero. The allowed values of n are therefore 1, 2, 3, 4, and so on. The angular quantum number (l) can be any integer between 0 and n – 1.

The superscript is the number of electrons in the level. For beryllium, there are two electrons in the 1s orbital and 2 electrons in the 2s orbital. The number in front of the energy level indicates relative energy. For example, 1s is lower energy than 2s, which in turn is lower energy than 2p.

Liters are larger than milliliters, so multiply by 1,000.