Bra-Ket Notation¶

SigSpace supports the Bra-ket notation to evaluate quantum states.

Possible syntax to use operators¶
No.	Syntax	Description
	`B = O\\|A> ket`	Applies the operator O to the state A and stores the result in a new state B.
	`C = bra <A\\\|B> ket`	Represents the inner product. The states A and B are multiplied and the integrated value is returned.
	`C = bra <A\\\|O\\\|B> ket`	Returns the expectation value calculated using the operator O. In many cases, A and B are identical, such as when determining the energy of a state.

The keywords “bra” and “ket” are needed to fulfill the python syntax and must be imported with from sigspace.H.braket import *. The import also includes the main operators:

Available operators¶

Default quantum mechanical operators¶
Python name	Name	Description
X	Position Operator	Is used to calculate the expected position of a particle.
I	Identity Operator	This is the “1” element of the operator algebra. Applied to a state it will return a copy of the state.
U	Time Operator	The time operator is used to obtain the time evolution of the state. It takes a value as parameter.
P	Momentum Operator	Computes the impulse of a wave function.
H	Hamiltonian	The hamiltonian of course is itself an operator. Its definition is explained in the first tutorials.
grad	Gradient Operator	Returns the first derivative of the wave function. .
laplace	Laplace Operator	The Laplace operator calculates the sum of the second derivative in all dimensions.