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from sympy.physics.pring import wavefunction, energy |
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from sympy.core.numbers import (I, pi) |
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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.integrals.integrals import integrate |
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from sympy.simplify.simplify import simplify |
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from sympy.abc import m, x, r |
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from sympy.physics.quantum.constants import hbar |
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def test_wavefunction(): |
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Psi = { |
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0: (1/sqrt(2 * pi)), |
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1: (1/sqrt(2 * pi)) * exp(I * x), |
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2: (1/sqrt(2 * pi)) * exp(2 * I * x), |
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3: (1/sqrt(2 * pi)) * exp(3 * I * x) |
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} |
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for n in Psi: |
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assert simplify(wavefunction(n, x) - Psi[n]) == 0 |
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def test_norm(n=1): |
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for i in range(n + 1): |
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assert integrate( |
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wavefunction(i, x) * wavefunction(-i, x), (x, 0, 2 * pi)) == 1 |
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def test_orthogonality(n=1): |
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for i in range(n + 1): |
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for j in range(i+1, n+1): |
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assert integrate( |
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wavefunction(i, x) * wavefunction(j, x), (x, 0, 2 * pi)) == 0 |
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def test_energy(n=1): |
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for i in range(n+1): |
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assert simplify( |
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energy(i, m, r) - ((i**2 * hbar**2) / (2 * m * r**2))) == 0 |
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