Chapter 7: Problem 14
Using the quantum particle in a box model, describe how the possible energies of the particle are related to the size of the box.
Chapter 7: Problem 14
Using the quantum particle in a box model, describe how the possible energies of the particle are related to the size of the box.
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Get started for freeA beam of mono-energetic protons with energy 2.0 MeV falls on a potential energy barrier of height \(20.0 \mathrm{MeV}\) and of width \(1.5 \mathrm{fm}\). What percentage of the beam is transmitted through the barrier?
Is it possible that when we measure the energy of a quantum particle in a box, the measurement may return a smaller value than the ground state energy? What is the highest value of the energy that we can measure for this particle?
A particle of mass \(m\) is confined to a box of width L. If the particle is in the first excited state, what are the probabilities of finding the particle in a region of width \(0.020 L\) around the given point \(x:\) (a) \(x=0.25 L ;\) (b) \(x=0.40 L ;(\mathrm{c}) x=0.75 L ;\) and (d) \(x=0.90 L\)
Can we measure both the position and momentum of a particle with complete precision?
Suppose an infinite square well extends from \(-L / 2\) to \(+L / 2 .\) Solve the time-independent Schrödinger's equation to find the allowed energies and stationary states of a particle with mass \(m\) that is confined to this well. Then show that these solutions can be obtained by making the coordinate transformation \(x^{\prime}=x-L / 2\) for the solutions obtained for the well extending between 0 and \(L\)
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