Effective mass of electron via energy
=====================================

In solid state physics, a particle's effective mass is the mass that it seems to have when responding to forces,
or the mass that it seems to have when interacting with other identical particles in a thermal distribution.
The effective mass is a quantity that is used to simplify band structures by modeling the behavior
of a free particle with that mass.

**Notation:**

#. :math:`\hbar` (:code:`hbar`) is :attr:`~symplyphysics.quantities.hbar`.

**Links:**

#. `Technische Universität Kiel, green box <https://www.tf.uni-kiel.de/matwis/amat/semi_en/kap_2/backbone/r2_3_1.html>`__.

#. `Wikipedia, fifth formula with adjustments <https://en.wikipedia.org/wiki/Effective_mass_(solid-state_physics)#Inertial_effective_mass_tensor>`__.

.. py:currentmodule:: symplyphysics.laws.condensed_matter.effective_mass_of_electron_via_energy

.. py:data:: effective_mass

    Effective :attr:`~symplyphysics.symbols.basic.mass` of the electron.

Symbol:
    :code:`m_eff`

Latex:
    :math:`m_\text{eff}`

Dimension:
    :code:`mass`


.. py:data:: angular_wavenumber

    :attr:`~symplyphysics.symbols.classical_mechanics.angular_wavenumber`.

Symbol:
    :code:`k`

Latex:
    :math:`k`

Dimension:
    :code:`angle/length`


.. py:data:: energy

    Electron energy as a function of angular wavenumber.

Symbol:
    :code:`E(k)`

Latex:
    :math:`E{\left(k \right)}`

Dimension:
    :code:`energy`


.. py:data:: law

    :code:`m_eff = hbar^2 / Derivative(E(k), (k, 2))`


    Latex:
        .. math::
            m_\text{eff} = \frac{\hbar^{2}}{\frac{d^{2}}{d k^{2}} E{\left(k \right)}}