feat(model): particle in a box

hamilflow/models/particle_in_box.py

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+from functools import cached_property
+from typing import Dict, List, Optional, Union
+
+import numpy as np
+import pandas as pd
+import scipy as sp
+from pydantic import BaseModel, Field, computed_field, field_validator
+
+
+PLANCK_CONST = 6.626e-34
+PI = 3.142
+
+
+class FiniteBox(BaseModel):
+    r"""Definition of the potential of the one dimensional box
+
+    For consistency, we always use $\mathbf x$ for displacement,
+    $L$ for box size.
+
+    The potential distribution we use is
+
+    $$
+    V(x)=\left\{\begin{array}{ll}
+    -V_{0} & |x|<L \\
+    0 & |x|>L
+    \end{array}\right.
+    $$
+
+    :cvar length: length of the box
+    :cvar p_height: potential well height
+    """
+
+    length: float = Field(ge=0)
+    p_height: float = Field(g=0, default=1.0)
+
+
+class QuantumParticle(BaseModel):
+    r"""Definition of the quantum particle
+
+    :cvar energy: energy of the particle
+    :cvar mass: weight of the particle
+    """
+
+    energy: float = Field(l=0, ge=-FiniteBox.p_height)
+    mass: float = Field(ge=0, default=1e-5)
+
+
+class WaveFunctionConst(BaseModel):
+    r"""Schrodinger equation simplification terms"""
+
+    @property
+    def h_bar(self) -> float:
+        """The hbar simplification
+        """
+        return PLANCK_CONST / (2 * PI)
+
+    @computed_field  # type: ignore[misc]
+    @cached_property
+    def calculate_alpha(self) -> float:
+        """Simplification term alpha
+
+        $$
+        \alpha=\sqrt{\frac{2 m}{\hbar^{2}}\left(V_{0}-|E|\right)}
+        $$
+        """
+        return (
+            np.sqrt(
+                2 * QuantumParticle.mass * (FiniteBox.p_height - np.abs(QuantumParticle.energy))
+                / (self.h_bar ** 2)
+            )
+        )
+
+    @computed_field  # type: ignore[misc]
+    @cached_property
+    def calculate_beta(self) -> float:
+        """Simplification term beta
+
+        $$
+        \beta=\sqrt{\frac{2 m}{\hbar^{2}}|E|}
+        $$
+        """
+        return (
+            np.sqrt(
+                2 * QuantumParticle.mass * np.abs(QuantumParticle.energy) / (self.h_bar ** 2)
+            )
+        )
+
+
+class ParticleInBox:
+    r"""Definition of the particle in a box quantum system
+
+    For consistency, we always use
+    $\mathbf x$ for displacement, $E$ for particle energy,
+    $V$ for barrier energy, and $L$ for box size.
+    The one-dimensional Schrödinger equation we are using is
+
+    $$
+    \begin{align}
+    -{\frac{\hbar^2}{2m}} {\frac{\partial^2 \psi}{\partial x^2}} + V(r) \psi = E \psi \label{eq1}
+    \end{align}
+    $$
+
+    And the even wave functions we are using are
+
+    $$
+    \psi^{F}(x)=\left\{\begin{array}{ll}
+    A \cos (\alpha \alpha) & 0<x<L \\
+    C e^{-\beta \hbar} & x>L
+    \end{array}\right.
+    $$
+
+    The odd wave functions we are using are
+
+    $$
+    \psi^{o}(x)=\left\{\begin{array}{ll}
+    A \sin (\alpha \alpha) & 0<x<L \\
+    C e^{-\beta_{x}} & x>L
+    \end{array}\right.
+    $$
+
+    References:
+
+    1. Particle in a box and tunneling. [cited 26 Mar 2024].
+        Available: https://chem.libretexts.org/Courses/University_of_California_Davis/UCD_Chem_110A%3A_Physical_Chemistry__I/UCD_Chem_110A%3A_Physical_Chemistry_I_(Koski)/Text/03%3A_The_Schrodinger_Equation/3.09%3A_Particle_in_a_Finite_Box_and_Tunneling_(optional)
+    2. Contributors to Wikimedia projects. Particle in a box.
+        In: Wikipedia [Internet]. 22 Jan 2024 [cited 26 Mar 2024].
+        Available: https://en.wikipedia.org/wiki/Particle_in_a_box
+
+    :param finite_box: the finite box definition
+    :param quantum_particle: the particle in the box
+    """
+
+    def __init__(
+        self,
+        finite_box: Dict[str, float],
+        quantum_particle: Dict[str, float],
+    ):
+        self.finite_box = FiniteBox.model_validate(finite_box)
+        self.quantum_particle = QuantumParticle.model_validate(quantum_particle)
+
+    def __call__(self) -> pd.DataFrame:
+        pass
+