| 1234567891011121314151617181920212223242526272829303132333435363738394041424344454647484950 |
- from sympy.core.numbers import (Rational, oo, pi)
- from sympy.core.singleton import S
- from sympy.core.symbol import Symbol
- from sympy.functions.elementary.exponential import exp
- from sympy.functions.elementary.miscellaneous import sqrt
- from sympy.integrals.integrals import integrate
- from sympy.simplify.simplify import simplify
- from sympy.abc import omega, m, x
- from sympy.physics.qho_1d import psi_n, E_n, coherent_state
- from sympy.physics.quantum.constants import hbar
- nu = m * omega / hbar
- def test_wavefunction():
- Psi = {
- 0: (nu/pi)**Rational(1, 4) * exp(-nu * x**2 /2),
- 1: (nu/pi)**Rational(1, 4) * sqrt(2*nu) * x * exp(-nu * x**2 /2),
- 2: (nu/pi)**Rational(1, 4) * (2 * nu * x**2 - 1)/sqrt(2) * exp(-nu * x**2 /2),
- 3: (nu/pi)**Rational(1, 4) * sqrt(nu/3) * (2 * nu * x**3 - 3 * x) * exp(-nu * x**2 /2)
- }
- for n in Psi:
- assert simplify(psi_n(n, x, m, omega) - Psi[n]) == 0
- def test_norm(n=1):
- # Maximum "n" which is tested:
- for i in range(n + 1):
- assert integrate(psi_n(i, x, 1, 1)**2, (x, -oo, oo)) == 1
- def test_orthogonality(n=1):
- # Maximum "n" which is tested:
- for i in range(n + 1):
- for j in range(i + 1, n + 1):
- assert integrate(
- psi_n(i, x, 1, 1)*psi_n(j, x, 1, 1), (x, -oo, oo)) == 0
- def test_energies(n=1):
- # Maximum "n" which is tested:
- for i in range(n + 1):
- assert E_n(i, omega) == hbar * omega * (i + S.Half)
- def test_coherent_state(n=10):
- # Maximum "n" which is tested:
- # test whether coherent state is the eigenstate of annihilation operator
- alpha = Symbol("alpha")
- for i in range(n + 1):
- assert simplify(sqrt(n + 1) * coherent_state(n + 1, alpha)) == simplify(alpha * coherent_state(n, alpha))
|
