occupation number

Since the occupation number for each fermion is 0 or 1, there are 2 possible basis states.

The are called the occupation number of the phonons.

This simplification is achieved with the occupation number representation.

This is why the formalism described here, is often referred to as the occupation number representation.

The space spanned by the occupation number basis is denoted the Fock space.

For bosons, the occupation numbers can take any integer values as long as their sum is equal to 'N'.

There is a one-to-one correspondence between the occupation number representation and valid boson states in the Fock space.

According to the Pauli exclusion principle, fermions cannot share quantum states, so their occupation numbers N can only take on the value 0 or 1.

Quantizing these oscillators, each level will have an integer occupation number, which will be the number of particles in it.

The eigenvalues of the response density matrix (which are the occupation numbers of the MP2 natural orbitals) can therefore be greater than 2 or negative.

Quantum theory can be formulated in terms of occupation numbers (amount of particles occupying one determined energy state) of these single-particle states.

Coherence then corresponds to a decrease in the occupation numbers of phonon modes and a decreased rate of inelastic scattering.

The occupation numbers are not limited to the range of zero to two, and therefore sometimes even the response density can be negative in certain regions of space.

The bosonic annihilation operator and creation operator are easily defined in the occupation number representation as having the following effects:

Physically, these matrices can be thought of as raising operators acting on a Hilbert space of n identical fermions in the occupation number basis.

Instead, in quantum theory the occupation numbers of the modes are quantized, cutting off the spectrum at high frequency in agreement with experimental observation and resolving the catastrophe.

Thus when we count the number of possible states of the system, we must count each and every microstate, and not just the possible sets of occupation numbers.

The number of ways that a set of occupation numbers can be realized is the product of the ways that each individual energy level can be populated:

The first step in second quantization is to express such quantum states in terms of occupation numbers, by listing the number of particles occupying each of the single-particle states etc.

The frequency ranges and intensities are determined by the magnetic moment of the nuclei that are observed, the applied magnetic field and temperature occupation number differences of the magnetic states.

The field's elementary degrees of freedom are the occupation numbers, and each occupation number is indexed by a number indicating which of the single-particle states it refers to:

For (far) infrared, microwave and radio frequency ranges the temperature dependent occupation numbers of states and the difference between Bose-Einstein statistics and Fermi-Dirac statistics determines the intensity of observed absorptions.

The ONETEP approach involves simultaneous optimization of the density kernel (a generalization of occupation numbers to non-orthogonal basis, which represents the density matrix in the basis of NGWFs) and the NGWFs themselves.

The bonding NBOs are of the "Lewis orbital"-type (occupation numbers near 2); antibonding NBOs are of the "non-Lewis orbital"-type (occupation numbers near 0).