def test_wavefunction():
Psi = {
0: (nu/pi)**(S(1)/4) * exp(-nu * x**2 /2),
1: (nu/pi)**(S(1)/4) * sqrt(2*nu) * x * exp(-nu * x**2 /2),
2: (nu/pi)**(S(1)/4) * (2 * nu * x**2 - 1)/sqrt(2) * exp(-nu * x**2 /2),
3: (nu/pi)**(S(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_wavefunction():
Psi = {
0: (nu/pi)**(S(1)/4) * exp(-nu * x**2 /2),
1: (nu/pi)**(S(1)/4) * sqrt(2*nu) * x * exp(-nu * x**2 /2),
2: (nu/pi)**(S(1)/4) * (2 * nu * x**2 - 1)/sqrt(2) * exp(-nu * x**2 /2),
3: (nu/pi)**(S(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_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_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
ls_sympy=l
# Mismo limites para scipy
li_scipy=0
ls_scipy=large
if Problem=='Harmonic oscilator':
large=0
if W.value=='':
omega=1
else:
omega=float(eval(W.value))
# Energías del oscilador armónico cuántico
En=E_n(n,w)
# Funciones de onda del oscilador armónico cuántico
Psin=psi_n(n,x,m,w)
# Límites del pozo definido de -oo a oo para sympy
li_sympy=-oo
ls_sympy=oo
# Límites del pozo definido de -oo a oo para scipy
li_scipy=-inf
ls_scipy=inf
if Problem=='Hydrogen atom (Helium correction)':
if atomic_number.value=='1 (Show Hydrogen energies)':
z=1
if atomic_number.value=='2 (Correct Helium first energy)':
z=2
large=0
omega=0
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_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
from sympy.physics.qho_1d import E_n, psi_n
from sympy.physics.sho import E_nl, R_nl
from sympy import var
var("x m omega")
var("r nu l")
x, y, z = symbols('x, y, z')
E_n(x, omega)
psi_n(2, x, m, omega)
E_nl(x, y, z)
R_nl(1, 0, 1, r)
R_nl(2, l, 1, r)