A quantum wave function specifies the state of an isolated system, and contains all possible information about it. O True O False

Suppose that you have a 2D quantum system where X and Px are the x- component position and momentum operators and Y and Py are the y- component position and momentum operators. Which of the following commutators is not equal to 0? [Py,Y] O IX,Y] O [Px,Px] O [PxY]

Which is not considered a wave function in the range in which it is defined?

make a quantum scheme that performs the addition of a pair of two-qubit numbers x and y modulo 4: |x, y> → |x, x + y mod 4>

The wave functions for the harmonic oscillators are 1 1 Y,(x) = th x)e zn the matrix element k[2,1]of the V2*n!"n kinetic energy is

Calculate the probability and probability density to find the particle between X = 0 and X = a /n when it is in the n state

Describe the property of quantum mechanical amplitude.

The figures below show the wave function describing two different states of a particle in an infinite square well. The number of nodes (within the well, but excluding the walls) in each wave function is related to the quantum number associated with the state it represents: Wave function A number of nodes = n-1 Wave function B M Determine the wavelength of the light absorbed by the particle in being excited from the state described by the wave function labelled A to the state described by the wave function labelled B. The distance between the two walls is 1.00 × 10-10 m and the mass of the particle is 1.82 × 10-30 kg. Enter the value of the wavelength in the empty box below. Your answer should be specified to an appropriate number of significant figures. wavelength = nm.

In the lab you make a simple harmonic oscillator with a 0.15-kg mass attached to a 12-N/m spring. (a) If the oscillation amplitude is 0.10 m, what is the corresponding quantum number n for the quantum harmonic oscillator? (b) What would be the amplitude of the quantum ground state for this oscillator? (c) What is the energy of a photon emitted when this oscillator makes a transition between adjacent energy levels? Comment on each of your results.