The discussion focuses on deriving the expression \(\partial_{\mu}Ae^{(-i/\hbar)x\bullet p}u(p)\). The user successfully applies the product rule of differentiation, resulting in the expression \(Ae^{(-i/\hbar)x\bullet p}u(p)[-i\hbar\partial_{\mu}(x^{\nu}p_{\nu})]\). The key challenge lies in recombining the components after differentiation, particularly the momentum four-vector \(p\). The solution confirms that the derivative can be explicitly calculated using established rules of calculus.
PREREQUISITESStudents and professionals in physics, particularly those studying quantum mechanics and advanced calculus, will benefit from this discussion. It is especially relevant for anyone working with wave functions and four-vector calculus.
[tex]\partial_{\mu}Ae^{(-i/\hbar)x\bullet p}u(p)<br /> =Ae^{(-i/\hbar)x\bullet p}u(p)[-i\hbar\partial_{\mu}(x^{\nu}p_{\nu})][/tex],ercagpince said:Homework Statement
I need to take the derivative of this expression explicitlyHomework Equations
[tex]\partial_{\mu}Ae^{(-i/\hbar)x\bullet p}u(p)[/tex]The Attempt at a Solution
I tried to take the derivative of it by taking the derivatives of components of the momentum four vector "p".
However, I got stuck while trying to recombine the expression left from derivation.