Dimensionality and default coordinates¶

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Dimensionality is to a large extent defined implicitly in Braketlab, meaning that there is no universal variable defining the dimensionality of integrals or visualization routines.

Rather, a ket has a number of coordinates associated with each dimension (and potentially various particles in the system). The default coordinates can be obtained as Sympy-variables as follows:

In [1]:

import braketlab as bk
import sympy as sp

x,y,z = bk.get_default_variables(0,3) #for particle p=0, get three default coordinates

x + y + z # display the variables in a sum

import braketlab as bk import sympy as sp x,y,z = bk.get_default_variables(0,3) #for particle p=0, get three default coordinates x + y + z # display the variables in a sum

Out[1]:

$\displaystyle x_{0; 0} + x_{0; 1} + x_{0; 2}$

Kets are initialized with a Sympy-function, from which the number of variables are taken as the dimensionality. Thus, for a one dimensional system we may do

In [2]:

p = bk.ket( sp.sin(2.0*x)*sp.exp(-.1*x**2) ) 

p.view(web = True)

p = bk.ket( sp.sin(2.0*x)*sp.exp(-.1*x**2) ) p.view(web = True)

Out[2]:

For a two-dimensional system, we have instead

In [3]:

p = bk.ket( x* sp.cos(0.2*(x**2 + y**2))*sp.exp(-.5*(x**2 + y**2)) ) 
p.view()

p = bk.ket( x* sp.cos(0.2*(x**2 + y**2))*sp.exp(-.5*(x**2 + y**2)) ) p.view()

Out[3]:

..and the three-dimensional case, which happens to be our own world:

In [4]:

p = bk.ket( x*y*sp.exp(-0.5*(x**2 + y**2 + z**2) ) )

p.view()

p = bk.ket( x*y*sp.exp(-0.5*(x**2 + y**2 + z**2) ) ) p.view()

Out[4]:

What is beyond the third dimension?¶

BraketLab is totally fine working in more than three dimensions, so feel free to define something like

In [5]:

x,y,z,w = bk.get_default_variables(0,4)

p = bk.ket( x*y*sp.exp(-0.5*(x**2 + y**2 + z**2 + w**2) ) )

x,y,z,w = bk.get_default_variables(0,4) p = bk.ket( x*y*sp.exp(-0.5*(x**2 + y**2 + z**2 + w**2) ) )

While the algebraic treatment is agnostic to the number of dimensions, the visualization can only handle up to three dimensions. Thus, calling

In [ ]:

p.view(web = True)

p.view(web = True)

... will only show a projection onto the first three dimensions.