Waves

Wave Function Exercise 1 Consider the Gaussian distribution $$ \rho(x) = Ae^{-\lambda(x - a)^2} $$ where $ A, a, \lambda $ are positive real constants. Use the normalization condition $\int_{-\infty}^{+\infty} \rho(x), dx = 1$ to determine $A$. Find $\langle x \rangle$, $\langle x^2 \rangle$, and the standard deviation $\sigma$. Sketch the graph of $\rho(x)$. Exercise 2 At time $ t = 0 $, a particle is represented by the wave function: ...