Usually generated math or science type content is consistently wrapped in $ or $$ tokens - which is then easy to render to Latex using method of choice. Today though I’m seeing a lot of instances where the math content is instead getting wrapped in parentheses or square brackets. Example response with this behaviour:

However, these interpretations might not be directly compatible with the classic expression E_v = h(v+1/2) used for a quantum harmonic oscillator unless E_c and E_g are redefined or specified to fit this scenario. If this were the case in a hypothetical or extended conceptual framework where:

- ( E_c ) could be defined as a base energy level (possibly of the ground state or zero-point energy).
- ( E_g ) could be considered an incremental energy term analogous to the quantum mechanical derivation between successive states.
Then, one could attempt to express E_v in these terms, provided the following relational concepts:

RedefinedE_c could represent the “ground state energy” of the quantum system described by ( E_{v=0} ) which would be ( E_0 = h \times \frac{1}{2} ).RedefinedE_g could represent the increase in energy per additional quantum number increment, which in the case of the quantum harmonic oscillator is ( h ).Given this non-standard but conceptual framework, one could write:

[ E_v = E_c + v \times E_g ]

Where:

- ( E_c = h \times \frac{1}{2} ) (reflects lowest possible energy state in this system)
- ( E_g = h ) (reflects the energy increment per quantum number unit)