Question
Use the Schrödinger equation to show that the expectation value of the kinetic energy of a particle is given by$$\left\langle E_{k}\right\rangle=\int_{-\infty}^{+\infty} \psi(x)\left(-\frac{\hbar^{2}}{2 m} \frac{d^{2} \psi(x)}{d x^{2}}\right) d x$$
Step 1
Step 1: The Schrödinger equation is given by $$ E\psi(x) = E_k\psi(x) + V(x)\psi(x) $$ where $E$ is the total energy, $E_k$ is the kinetic energy, $V(x)$ is the potential energy, and $\psi(x)$ is the wave function. Show more…
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