📘 quantum mechanics

1. **Problem Statement:** Determine if each given function is normalized over its specified domain and volume element. If not normalized, find the normalization constant $N$ such t

1. **Problem Statement:** We need to determine which of the three proposed wavefunctions is physically acceptable for a one-dimensional quantum system defined on the interval $x \g

1. **Problem Statement:** We are given the 2p orbital wavefunctions of the hydrogen atom:

1. **Problem Statement:** Show that the Schrödinger equation $$-\frac{\hbar^2}{2m} \frac{\partial^2 \phi(x,t)}{\partial x^2} = -i \hbar \frac{\partial \phi(x,t)}{\partial t}$$

1. **Problem Statement:** Show that the Schrödinger equation $$-\frac{\hbar^2}{2m} \frac{\partial^2 \phi(x,t)}{\partial x^2} = -i \hbar \frac{\partial \phi(x,t)}{\partial t}$$

1. **State the problem:** We want to show that $$Q = \left(\frac{\partial}{\partial t} - \frac{H}{\hbar}\right)\Psi$$ where $\Psi$ is a wavefunction, $H$ is the Hamiltonian operato