51 lines
1.7 KiB
Python
51 lines
1.7 KiB
Python
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from sympy.core.numbers import (Rational, oo, pi)
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from sympy.core.singleton import S
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from sympy.core.symbol import Symbol
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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 omega, m, x
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from sympy.physics.qho_1d import psi_n, E_n, coherent_state
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from sympy.physics.quantum.constants import hbar
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nu = m * omega / hbar
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def test_wavefunction():
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Psi = {
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0: (nu/pi)**Rational(1, 4) * exp(-nu * x**2 /2),
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1: (nu/pi)**Rational(1, 4) * sqrt(2*nu) * x * exp(-nu * x**2 /2),
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2: (nu/pi)**Rational(1, 4) * (2 * nu * x**2 - 1)/sqrt(2) * exp(-nu * x**2 /2),
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3: (nu/pi)**Rational(1, 4) * sqrt(nu/3) * (2 * nu * x**3 - 3 * x) * exp(-nu * x**2 /2)
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}
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for n in Psi:
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assert simplify(psi_n(n, x, m, omega) - Psi[n]) == 0
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def test_norm(n=1):
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# Maximum "n" which is tested:
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for i in range(n + 1):
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assert integrate(psi_n(i, x, 1, 1)**2, (x, -oo, oo)) == 1
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def test_orthogonality(n=1):
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# Maximum "n" which is tested:
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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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psi_n(i, x, 1, 1)*psi_n(j, x, 1, 1), (x, -oo, oo)) == 0
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def test_energies(n=1):
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# Maximum "n" which is tested:
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for i in range(n + 1):
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assert E_n(i, omega) == hbar * omega * (i + S.Half)
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def test_coherent_state(n=10):
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# Maximum "n" which is tested:
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# test whether coherent state is the eigenstate of annihilation operator
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alpha = Symbol("alpha")
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for i in range(n + 1):
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assert simplify(sqrt(n + 1) * coherent_state(n + 1, alpha)) == simplify(alpha * coherent_state(n, alpha))
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