switching to high quality piper tts and added label translations

2026-01-29 23:48:19 +01:00
commit d80c619df9
3934 changed files with 1451600 additions and 0 deletions
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+from sympy.core import S, pi, Rational
+from sympy.functions import hermite, sqrt, exp, factorial, Abs
+from sympy.physics.quantum.constants import hbar
+
+
+def psi_n(n, x, m, omega):
+    """
+    Returns the wavefunction psi_{n} for the One-dimensional harmonic oscillator.
+
+    Parameters
+    ==========
+
+    n :
+        the "nodal" quantum number.  Corresponds to the number of nodes in the
+        wavefunction.  ``n >= 0``
+    x :
+        x coordinate.
+    m :
+        Mass of the particle.
+    omega :
+        Angular frequency of the oscillator.
+
+    Examples
+    ========
+
+    >>> from sympy.physics.qho_1d import psi_n
+    >>> from sympy.abc import m, x, omega
+    >>> psi_n(0, x, m, omega)
+    (m*omega)**(1/4)*exp(-m*omega*x**2/(2*hbar))/(hbar**(1/4)*pi**(1/4))
+
+    """
+
+    # sympify arguments
+    n, x, m, omega = map(S, [n, x, m, omega])
+    nu = m * omega / hbar
+    # normalization coefficient
+    C = (nu/pi)**Rational(1, 4) * sqrt(1/(2**n*factorial(n)))
+
+    return C * exp(-nu* x**2 /2) * hermite(n, sqrt(nu)*x)
+
+
+def E_n(n, omega):
+    """
+    Returns the Energy of the One-dimensional harmonic oscillator.
+
+    Parameters
+    ==========
+
+    n :
+        The "nodal" quantum number.
+    omega :
+        The harmonic oscillator angular frequency.
+
+    Notes
+    =====
+
+    The unit of the returned value matches the unit of hw, since the energy is
+    calculated as:
+
+        E_n = hbar * omega*(n + 1/2)
+
+    Examples
+    ========
+
+    >>> from sympy.physics.qho_1d import E_n
+    >>> from sympy.abc import x, omega
+    >>> E_n(x, omega)
+    hbar*omega*(x + 1/2)
+    """
+
+    return hbar * omega * (n + S.Half)
+
+
+def coherent_state(n, alpha):
+    """
+    Returns <n|alpha> for the coherent states of 1D harmonic oscillator.
+    See https://en.wikipedia.org/wiki/Coherent_states
+
+    Parameters
+    ==========
+
+    n :
+        The "nodal" quantum number.
+    alpha :
+        The eigen value of annihilation operator.
+    """
+
+    return exp(- Abs(alpha)**2/2)*(alpha**n)/sqrt(factorial(n))