def test_differential_operator(): x = Symbol('x') f = Function('f') d = DifferentialOperator(Derivative(f(x), x), f(x)) g = Wavefunction(x**2, x) assert qapply(d*g) == Wavefunction(2*x, x) assert d.expr == Derivative(f(x), x) assert d.function == f(x) assert d.variables == (x,) assert diff(d, x) == DifferentialOperator(Derivative(f(x), x, 2), f(x)) d = DifferentialOperator(Derivative(f(x), x, 2), f(x)) g = Wavefunction(x**3, x) assert qapply(d*g) == Wavefunction(6*x, x) assert d.expr == Derivative(f(x), x, 2) assert d.function == f(x) assert d.variables == (x,) assert diff(d, x) == DifferentialOperator(Derivative(f(x), x, 3), f(x)) d = DifferentialOperator(1/x*Derivative(f(x), x), f(x)) assert d.expr == 1/x*Derivative(f(x), x) assert d.function == f(x) assert d.variables == (x,) assert diff(d, x) == \ DifferentialOperator(Derivative(1/x*Derivative(f(x), x), x), f(x)) assert qapply(d*g) == Wavefunction(3*x, x) # 2D cartesian Laplacian y = Symbol('y') d = DifferentialOperator(Derivative(f(x, y), x, 2) + \ Derivative(f(x, y), y, 2), f(x, y)) w = Wavefunction(x**3*y**2 + y**3*x**2, x, y) assert d.expr == Derivative(f(x, y), x, 2) + Derivative(f(x, y), y, 2) assert d.function == f(x, y) assert d.variables == (x, y) assert diff(d, x) == \ DifferentialOperator(Derivative(d.expr, x), f(x, y)) assert diff(d, y) == \ DifferentialOperator(Derivative(d.expr, y), f(x, y)) assert qapply(d*w) == Wavefunction(2*x**3 + 6*x*y**2 + 6*x**2*y + 2*y**3, \ x, y) # 2D polar Laplacian (th = theta) r, th = symbols('r th') d = DifferentialOperator(1/r*Derivative(r*Derivative(f(r, th), r) , r) + \ 1/(r**2)*Derivative(f(r, th), th, 2), f(r, th)) w = Wavefunction(r**2*sin(th), r, (th, 0, pi)) assert d.expr == \ 1/r*Derivative(r*Derivative(f(r, th), r), r) + \ 1/(r**2)*Derivative(f(r, th), th, 2) assert d.function == f(r, th) assert d.variables == (r, th) assert diff(d, r) == \ DifferentialOperator(Derivative(d.expr, r), f(r, th)) assert diff(d, th) == \ DifferentialOperator(Derivative(d.expr, th), f(r, th)) assert qapply(d*w) == Wavefunction(3*sin(th), r, (th, 0, pi))
def test_sympy__physics__quantum__state__Wavefunction(): from sympy.physics.quantum.state import Wavefunction from sympy.functions import sin from sympy import Piecewise, pi n = 1 L = 1 g = Piecewise((0, x < 0), (0, x > L), (sqrt(2 // L) * sin(n * pi * x / L), True)) assert _test_args(Wavefunction(g, x))
def _apply_operator_Wavefunction(self, func): from sympy.physics.quantum.state import Wavefunction var = self.variables wf_vars = func.args[1:] f = self.function new_expr = self.expr.subs(f, func(*var)) new_expr = new_expr.doit() return Wavefunction(new_expr, *wf_vars)
def test_wavefunction(): x, y, L = symbols('x,y,L', real=True) n = symbols('n', integer=True) f = Wavefunction(x**2, x) p = f.prob() lims = f.limits assert f.is_normalized is False assert f.norm == oo assert f(10) == 100 assert p(10) == 10000 assert lims[x] == (-oo, oo) assert diff(f, x) == Wavefunction(2*x, x) raises(NotImplementedError, lambda: f.normalize()) assert conjugate(f) == Wavefunction(conjugate(f.expr), x) assert conjugate(f) == Dagger(f) g = Wavefunction(x**2*y + y**2*x, (x, 0, 1), (y, 0, 2)) lims_g = g.limits assert lims_g[x] == (0, 1) assert lims_g[y] == (0, 2) assert g.is_normalized is False assert g.norm == sqrt(42)/3 assert g(2, 4) == 0 assert g(1, 1) == 2 assert diff(diff(g, x), y) == Wavefunction(2*x + 2*y, (x, 0, 1), (y, 0, 2)) assert conjugate(g) == Wavefunction(conjugate(g.expr), *g.args[1:]) assert conjugate(g) == Dagger(g) h = Wavefunction(sqrt(5)*x**2, (x, 0, 1)) assert h.is_normalized is True assert h.normalize() == h assert conjugate(h) == Wavefunction(conjugate(h.expr), (x, 0, 1)) assert conjugate(h) == Dagger(h) piab = Wavefunction(sin(n*pi*x/L), (x, 0, L)) assert piab.norm == sqrt(L/2) assert piab(L + 1) == 0 assert piab(0.5) == sin(0.5*n*pi/L) assert piab(0.5, n=1, L=1) == sin(0.5*pi) assert piab.normalize() == \ Wavefunction(sqrt(2)/sqrt(L)*sin(n*pi*x/L), (x, 0, L)) assert conjugate(piab) == Wavefunction(conjugate(piab.expr), (x, 0, L)) assert conjugate(piab) == Dagger(piab) k = Wavefunction(x**2, 'x') assert type(k.variables[0]) == Symbol
def test_wavefunction(): x, y = symbols('x y', real=True) L = symbols('L', positive=True) n = symbols('n', integer=True, positive=True) f = Wavefunction(x**2, x) p = f.prob() lims = f.limits assert f.is_normalized is False assert f.norm is oo assert f(10) == 100 assert p(10) == 10000 assert lims[x] == (-oo, oo) assert diff(f, x) == Wavefunction(2 * x, x) raises(NotImplementedError, lambda: f.normalize()) assert conjugate(f) == Wavefunction(conjugate(f.expr), x) assert conjugate(f) == Dagger(f) g = Wavefunction(x**2 * y + y**2 * x, (x, 0, 1), (y, 0, 2)) lims_g = g.limits assert lims_g[x] == (0, 1) assert lims_g[y] == (0, 2) assert g.is_normalized is False assert g.norm == sqrt(42) / 3 assert g(2, 4) == 0 assert g(1, 1) == 2 assert diff(diff(g, x), y) == Wavefunction(2 * x + 2 * y, (x, 0, 1), (y, 0, 2)) assert conjugate(g) == Wavefunction(conjugate(g.expr), *g.args[1:]) assert conjugate(g) == Dagger(g) h = Wavefunction(sqrt(5) * x**2, (x, 0, 1)) assert h.is_normalized is True assert h.normalize() == h assert conjugate(h) == Wavefunction(conjugate(h.expr), (x, 0, 1)) assert conjugate(h) == Dagger(h) piab = Wavefunction(sin(n * pi * x / L), (x, 0, L)) assert piab.norm == sqrt(L / 2) assert piab(L + 1) == 0 assert piab(0.5) == sin(0.5 * n * pi / L) assert piab(0.5, n=1, L=1) == sin(0.5 * pi) assert piab.normalize() == \ Wavefunction(sqrt(2)/sqrt(L)*sin(n*pi*x/L), (x, 0, L)) assert conjugate(piab) == Wavefunction(conjugate(piab.expr), (x, 0, L)) assert conjugate(piab) == Dagger(piab) k = Wavefunction(x**2, 'x') assert type(k.variables[0]) == Symbol