The discussion centers on the form of the wave function for a free particle, represented as ψ(x,t) = e^(i(kx - wt)), and its compliance with the Schrödinger Equation (SE). The participant derives the relationship w = hk²/(4πm) when substituting into the SE. However, they question the validity of this expression, specifically whether the energy E = ħω aligns correctly with the derived terms, noting a potential discrepancy with the presence of an extra ħ in the calculations.
PREREQUISITESStudents of quantum mechanics, physicists analyzing wave functions, and anyone studying the mathematical foundations of the Schrödinger Equation.
There's one hbar too many in there, no?christianjb said:w = hbar^2 k^2 / 2m