python - 如何将 SymPy 的 DifferentialOperator 应用于另一个运算符？

Question

假设我有这样的东西:

from sympy.physics.quantum import *
from sympy import symbols, Function, Derivative, var
m = symbols('mu', positive=True)
var('x')
var('t')
f = Function('psi')
T = DifferentialOperator(-1 / (2 * m) * Derivative('psi(x,t)', x, x))
V = Operator('V(x)')
K = Operator('K(x)')

如何获得 [T,K]u(x,t) = T(K(u)) - K(T(u)) 的表达式？这里，u是波函数，T应该将链式法则应用于K(u)乘积。

Answer 1

好吧，一个解决方法:

from sympy import symbols, Function, Derivative, var, init_printing

def T(y):
    var('mu')
    return -1 / (2 * mu) * Derivative(y, x, x)

def V(y):
    var('x')
    V = Function('V', commutative=True)(x)
    return V * y

def comm(A, B):
    def comm(y):
        return A(B(y)) - B(A(y))
    return comm

var('x')
var('t')
f = Function('psi', commutative=False)
comm(T, V)(f)