3-gram ball is bouncing between two walls separated by 15 cm with a velocity equal to 0.5 mm/s. If this system is an infinite square well, find the quantum nu
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A 3-gram ball is bouncing between two walls separated by 15 cm with a velocity equal to 0.5 mm/s. If this system is an infinite square well, find the quantum number (n).
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- The wave function of a particle in a one-dimensional box of width L is u(x) = A sin (7x/L). If we know the particle must be somewhere in the box, what must be the value of A?Particle of mass m moves in a three-dimensional box with edge lengths L1, L2, and L3. (a) Find the energies of the six lowest states if L1 =L, L2 = 2L, and L3 = 2L. (b) Which if these energies are degenerate?a question of quantum mechanics: Consider a particle in a two-dimensional potential as shown in the picture Suppose the particle is in the ground state. If we measure the position of the particle, what isthe probability of detecting it in region 0<=x,y<=L/2 ?
- 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]Chapter 39, Problem 009 Suppose that an electron trapped in a one-dimensional infinite well of width 144 pm is excited from its first excited state to the state with n 9. (a) What energy must be transferred to the electron for this quantum jump? The electron then de- excites back to its ground state by emitting light. In the various possible ways it can do this, what are the (b) shortest, (c) second shortest, (d) longest, and (e) second longest wavelengths that can be emitted? (a) Number Units (b) Number Units (c) Number Units (d) Number Units (e) Number UnitsClearly explain why the quantum oscillator is a good model for representing molecular vibrations.
- 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.