Creating a ket¶

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Many standard textbook functions can be obtained from the basisbank-submodule, but creating custom kets from sympy expressions is straight forward.

...from Basisbank¶

For instance, to obtain a predefined basisbank S-type Slater orbital you may do as follows:

In [1]:

import braketlab as bk

exponent = 2.0
weight = 1.0
quantum_number_n = 1.0
quantum_number_l = 2.0
quantum_number_m = 0.0

psi_0 = bk.basisbank.get_sto(exponent,weight,quantum_number_n,quantum_number_l,quantum_number_m) # a Slater type orbital
psi_0

import braketlab as bk exponent = 2.0 weight = 1.0 quantum_number_n = 1.0 quantum_number_l = 2.0 quantum_number_m = 0.0 psi_0 = bk.basisbank.get_sto(exponent,weight,quantum_number_n,quantum_number_l,quantum_number_m) # a Slater type orbital psi_0

Out[1]:

$\vert \chi_{2,0}^{2.00} \rangle$

In [2]:

psi_0.ket_sympy_expression # show the sympy-expression

psi_0.ket_sympy_expression # show the sympy-expression

Out[2]:

$\displaystyle 1.0 \cdot \left(8.48528137423857 x_{0; 2}^{2.0} - 2.82842712474619 \left(x_{0; 0}^{2.0} + x_{0; 1}^{2.0} + x_{0; 2}^{2.0}\right)^{1.0}\right) e^{- \sqrt{x_{0; 0}^{2.0} + x_{0; 1}^{2.0} + x_{0; 2}^{2.0}} \cdot 2.0}$

In [3]:

psi_0.view() # create a view (open the visualization module Evince)

psi_0.view() # create a view (open the visualization module Evince)

Out[3]:

...or from scratch¶

If you would like to instead manually define your ket, you'll have to initialize it from a Sympy-function as follows:

In [4]:

import braketlab as bk
import sympy as sp

x,y,z = bk.get_default_variables(0,3)   # Particle 0 has 3 coordinates
                                        # This is not strictly necessary, but a safer solution for book-keping many body systems

p = bk.ket( x*sp.sin(2.0*y)/(x**2 + y**2 + z**2)**2, name = "\\varphi" )
p

import braketlab as bk import sympy as sp x,y,z = bk.get_default_variables(0,3) # Particle 0 has 3 coordinates # This is not strictly necessary, but a safer solution for book-keping many body systems p = bk.ket( x*sp.sin(2.0*y)/(x**2 + y**2 + z**2)**2, name = "\\varphi" ) p

Out[4]:

$\vert \varphi \rangle$

In [5]:

p.ket_sympy_expression

p.ket_sympy_expression

Out[5]:

$\displaystyle \frac{1.0 x_{0; 0} \sin{\left(2.0 x_{0; 1} \right)}}{\left(x_{0; 0}^{2} + x_{0; 1}^{2} + x_{0; 2}^{2}\right)^{2}}$

In [6]:

p.view()

p.view()

Out[6]:

In [ ]: