Consider the Gaussian wave packet, v(2) = A exp Poz -a %3D where po and & are real parameters. a. Show that this wave function can be normalized, dr |ú(r)² = 1, and find the corresponding amplitude A. b. Find the corresponding wave function, o(p), in the momentum repre- sentation and check its normalization. c. Calculate expectation values (r) and (p).

Consider the Gaussian wave packet, v(2) = A exp Poz -a %3D where po and & are real parameters. a. Show that this wave function can be normalized, dr |ú(r)² = 1, and find the corresponding amplitude A. b. Find the corresponding wave function, o(p), in the momentum repre- sentation and check its normalization. c. Calculate expectation values (r) and (p).

Similar questions

No Spacing Heading 1 Normal Aa v A A 困、 Paragraph Styles The action along a path is defined to be: S = [(K.E.-P. E.) dt Determine the physical units of action. Detail Feynman's approach to calculating the probability amplitude for an electron to go from one event A to another B using the "sum over all paths". A'Focus 12 1> 12
A particle with mass m is in the state .2 mx +iat 2h Y(x,t) = Ae where A and a are positive real constants. Calculate the expectation values of (x).
Consider the wavefunction Y(x) = exp(-2a|x|). a) Normalize the above wavefunction. b) Sketch the probability density of the above wavefunction. c) What is the probability of finding the particle in the range 0 < x s 1/a ?
Question A2 Consider an infinite square well of width L, with V = 0 in the region -L/2 < x < L/2 and V → ∞ everywhere else. For this system: a) Write down and solve the time-independent Schrödinger equation for & inside the well, where -L/2< x