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"""Tests for cartesian.py""" |
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from sympy.core.numbers import (I, pi) |
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from sympy.core.singleton import S |
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from sympy.core.symbol import symbols |
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from sympy.functions.elementary.exponential import exp |
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from sympy.functions.elementary.miscellaneous import sqrt |
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from sympy.functions.special.delta_functions import DiracDelta |
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from sympy.sets.sets import Interval |
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from sympy.testing.pytest import XFAIL |
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from sympy.physics.quantum import qapply, represent, L2, Dagger |
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from sympy.physics.quantum import Commutator, hbar |
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from sympy.physics.quantum.cartesian import ( |
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XOp, YOp, ZOp, PxOp, X, Y, Z, Px, XKet, XBra, PxKet, PxBra, |
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PositionKet3D, PositionBra3D |
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) |
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from sympy.physics.quantum.operator import DifferentialOperator |
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x, y, z, x_1, x_2, x_3, y_1, z_1 = symbols('x,y,z,x_1,x_2,x_3,y_1,z_1') |
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px, py, px_1, px_2 = symbols('px py px_1 px_2') |
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def test_x(): |
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assert X.hilbert_space == L2(Interval(S.NegativeInfinity, S.Infinity)) |
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assert Commutator(X, Px).doit() == I*hbar |
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assert qapply(X*XKet(x)) == x*XKet(x) |
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assert XKet(x).dual_class() == XBra |
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assert XBra(x).dual_class() == XKet |
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assert (Dagger(XKet(y))*XKet(x)).doit() == DiracDelta(x - y) |
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assert (PxBra(px)*XKet(x)).doit() == \ |
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exp(-I*x*px/hbar)/sqrt(2*pi*hbar) |
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assert represent(XKet(x)) == DiracDelta(x - x_1) |
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assert represent(XBra(x)) == DiracDelta(-x + x_1) |
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assert XBra(x).position == x |
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assert represent(XOp()*XKet()) == x*DiracDelta(x - x_2) |
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assert represent(XBra("y")*XKet()) == DiracDelta(x - y) |
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assert represent( |
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XKet()*XBra()) == DiracDelta(x - x_2) * DiracDelta(x_1 - x) |
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rep_p = represent(XOp(), basis=PxOp) |
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assert rep_p == hbar*I*DiracDelta(px_1 - px_2)*DifferentialOperator(px_1) |
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assert rep_p == represent(XOp(), basis=PxOp()) |
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assert rep_p == represent(XOp(), basis=PxKet) |
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assert rep_p == represent(XOp(), basis=PxKet()) |
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assert represent(XOp()*PxKet(), basis=PxKet) == \ |
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hbar*I*DiracDelta(px - px_2)*DifferentialOperator(px) |
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@XFAIL |
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def _text_x_broken(): |
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assert represent(XOp()*XKet()*XBra('y')) == \ |
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x*DiracDelta(x - x_3)*DiracDelta(x_1 - y) |
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def test_p(): |
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assert Px.hilbert_space == L2(Interval(S.NegativeInfinity, S.Infinity)) |
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assert qapply(Px*PxKet(px)) == px*PxKet(px) |
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assert PxKet(px).dual_class() == PxBra |
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assert PxBra(x).dual_class() == PxKet |
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assert (Dagger(PxKet(py))*PxKet(px)).doit() == DiracDelta(px - py) |
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assert (XBra(x)*PxKet(px)).doit() == \ |
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exp(I*x*px/hbar)/sqrt(2*pi*hbar) |
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assert represent(PxKet(px)) == DiracDelta(px - px_1) |
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rep_x = represent(PxOp(), basis=XOp) |
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assert rep_x == -hbar*I*DiracDelta(x_1 - x_2)*DifferentialOperator(x_1) |
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assert rep_x == represent(PxOp(), basis=XOp()) |
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assert rep_x == represent(PxOp(), basis=XKet) |
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assert rep_x == represent(PxOp(), basis=XKet()) |
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assert represent(PxOp()*XKet(), basis=XKet) == \ |
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-hbar*I*DiracDelta(x - x_2)*DifferentialOperator(x) |
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assert represent(XBra("y")*PxOp()*XKet(), basis=XKet) == \ |
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-hbar*I*DiracDelta(x - y)*DifferentialOperator(x) |
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def test_3dpos(): |
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assert Y.hilbert_space == L2(Interval(S.NegativeInfinity, S.Infinity)) |
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assert Z.hilbert_space == L2(Interval(S.NegativeInfinity, S.Infinity)) |
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test_ket = PositionKet3D(x, y, z) |
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assert qapply(X*test_ket) == x*test_ket |
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assert qapply(Y*test_ket) == y*test_ket |
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assert qapply(Z*test_ket) == z*test_ket |
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assert qapply(X*Y*test_ket) == x*y*test_ket |
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assert qapply(X*Y*Z*test_ket) == x*y*z*test_ket |
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assert qapply(Y*Z*test_ket) == y*z*test_ket |
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assert PositionKet3D() == test_ket |
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assert YOp() == Y |
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assert ZOp() == Z |
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assert PositionKet3D.dual_class() == PositionBra3D |
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assert PositionBra3D.dual_class() == PositionKet3D |
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other_ket = PositionKet3D(x_1, y_1, z_1) |
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assert (Dagger(other_ket)*test_ket).doit() == \ |
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DiracDelta(x - x_1)*DiracDelta(y - y_1)*DiracDelta(z - z_1) |
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assert test_ket.position_x == x |
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assert test_ket.position_y == y |
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assert test_ket.position_z == z |
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assert other_ket.position_x == x_1 |
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assert other_ket.position_y == y_1 |
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assert other_ket.position_z == z_1 |
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