plot画分段函数_零三：分段函数，连不等式的实现，一元函数定积分

#分段函数：sympy.Piecewise((表达式, 条件)...)
#与运算：sympy.And(...)，注意sympy不可以-1<x<1
#定积分：sympy.integrate(f,(val1,i1,f1)...)

import sympy
import matplotlib.pyplot as plt
pi=sympy.pi

x=sympy.Symbol('x')
def Psi(n): #一维无限深势阱
    if n%2:
        f=sympy.cos(n*pi*x/2)
    else:
        f=sympy.sin(n*pi*x/2)
    return sympy.Piecewise((f,sympy.And(-1<x,x<1)),(0,True))

Psi1=Psi(4)
z=[-1.1+0.01*_ for _ in range(221)]
y=list(map(lambda k:float(Psi1.evalf(subs={x:k})**2),z))
plt.cla()
plt.plot(z,y)
plt.show()

print(sympy.integrate(Psi(4)*Psi(3),(x,-1,1)))
#0
print(sympy.integrate(Psi(4)*Psi(4),(x,-1,1)))
#1