probabilities¶

libra_py.probabilities.Boltz_cl_prob(E, T)[source]¶

Computes the normalized classical Boltzmann probability distribution function

Parameters

E (double) – the minimum energy level [in a.u.]
T (double) – temperature [K]

Returns

The probability to have kinetic energy greater than a given threshold value at: given temperature

Return type

double

See also

This is essentially a Maxwell-Boltzmann distribution in the energy scale Used this: http://mathworld.wolfram.com/MaxwellDistribution.html

libra_py.probabilities.Boltz_quant_prob(E, T)[source]¶

Computes the quantum Boltzman probability of occupying different energy levels at given temperature T: P_i = exp(-E_i/kT) / Z where Z = sum_i { exp(-E_i/kT) }

Parameters

E (list of doubles) – energy levels [in a.u.]
T (double) – temperature [K]

Returns

prob: the probability to find a system in a discrete state i with: energy E_i at given temperature T, considering a number of selected energy levels as given by the list E

Return type

double

libra_py.probabilities.HO_prob(E, qn, T)[source]¶

Probability that the oscillators are in the given vibrational states Multi-oscillator generalization of Eq. 10

Parameters

E (list of doubles) – all the energy levels present in the system [in a.u.]
qn (list of ints) – quantum numbers for each oscillator
T (double) – temperature

Returns

(res, prob), where:

res ( double ): the probability that the system of N oscillators is in a given
state, defined by quantum numbers of each oscillator

prob ( list of N doubles ): probability with which each of N oscillators occupies
given vibrational state

Return type

tuple

libra_py.probabilities.HO_prob_E_up(E, Emin, T)[source]¶

We will compute the probability that a system of N oscillators has energy more or equal of Emin. The oscillators can have only quantized energy values

Parameters

E (list of doubles) – all the energy levels present in the system [in a.u.]
Emin (double) – the minimum energy
T (double) – temperature [K]

Note

This function is not yet implemented

libra_py.probabilities.HO_prob_up(E, qn, T)[source]¶

Probability that the oscillators are in vibrational states with quantum numbers above or equal to the minimal quantum numbers provided. Multi-oscillator generalization of Eq. 12

Parameters

E (list of doubles) – all the energy levels present in the system [in a.u.]
qn (list of ints) – min quantum numbers for each frequency
T (double) – temperature [K]

Returns

(res, prob), where:

res ( double ): the probability that the system of N oscillators is in any state
higher than given quantum numbers of each oscillators

prob ( list of N doubles ): probability with which each oscillator can be found in any of
the vibrational states higher than given by the quantum numbers in the qn argument

Return type

tuple