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 — documentation:basics:wave_functions [2016/10/10 09:40] (current) 2016/10/06 20:35 Maurits W. Haverkort created 2016/10/06 20:35 Maurits W. Haverkort created Line 1: Line 1: + {{indexmenu_n>​3}} + ====== Wave functions ====== + ### + Wave-functions can be created from a string containing 1's (occupied) and 0's (unoccupied). For each Fermionic spin-orbital on has one bit. For Bosonic modes Quanty reserves 8 bit, i.e. Bosons can have an occupation from 0 to 255. A wave-function resembling a single electron in a $p_x$ orbital with spin-up could be created by defining 6 spin-orbitals,​ creating two lists of length 3 for spin-up and spin-down and by creating a wave function that is a linear combination of $m_l=1$ and $m_l=-1$. + ​ + -- a number of Fermionic modes or spin-orbitals + NF=6 + -- a number of Bosonic modes (phonon modes, ...) + NB=0 + + -- For a p-shell we would like the have 6 + -- spinorbitals with the quantum numbers ​ + -- spin down ml=-1,​ml=0,​ml=1 and + -- spin up with ml=-1, ml=0, ml=1 + -- We can group different spin-orbitals into + -- lists and assign meaning to them + IndexDn={0,​2,​4} + IndexUp={1,​3,​5} + -- the code knows that a 3 fold degenerate shell + -- has l=1 and ml=-1, 0 and 1 are + -- assigned to them automatically + + -- the wave-function with one electron in the + -- px orbital with spin down is created as + psipx = NewWavefunction(NF,​ NB, {{"​100000",​math.sqrt(1/​2)},​ {"​000010",​math.sqrt(1/​2)}}) + ​ + ### + + + ===== Index ===== + - [[documentation:​basics:​basis|]] + - [[documentation:​basics:​operators|]] + - Wavefunctions + - [[documentation:​basics:​expectation_values|]] + - [[documentation:​basics:​eigen_states|]] + - [[documentation:​basics:​spectra|]] + - [[documentation:​basics:​resonant_spectra|]] + - [[documentation:​basics:​fluorescence_yield|]]

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