A particle is trapped into a potential well centered on the position x = 0, of length R. Inside the well, the value of the potential is zero. Outside of the well, the potential is infinite. Draw a schema of the problem, and define all axes you may need to solve the problem Give the Schrodinger equation of the wave function of that particle, explaining all terms involved into the equation. ) What are the proper values of the energy of this particle? We will assume that the energy of the particle is all the time positive, and we will use the quantum number n for the states of energy. We will assume we are able to measure the energy of the particle with a given precision. Show that there is a maximal precision you can obtain. If you want to be able to measure the difference between two states of energy (i.e. the difference between two energy levels), your precision needs to be about half of the difference you are trying to measure. Deduce from the previous question that there is a relation between n and R in order to be able to measure AE = En+1 — En - Would the results be the same if inside the well, the potential value was V = -10?
A particle is trapped into a potential well centered on the position x = 0, of length R. Inside the well, the value of the potential is zero. Outside of the well, the potential is infinite. Draw a schema of the problem, and define all axes you may need to solve the problem Give the Schrodinger equation of the wave function of that particle, explaining all terms involved into the equation. ) What are the proper values of the energy of this particle? We will assume that the energy of the particle is all the time positive, and we will use the quantum number n for the states of energy. We will assume we are able to measure the energy of the particle with a given precision. Show that there is a maximal precision you can obtain. If you want to be able to measure the difference between two states of energy (i.e. the difference between two energy levels), your precision needs to be about half of the difference you are trying to measure. Deduce from the previous question that there is a relation between n and R in order to be able to measure AE = En+1 — En - Would the results be the same if inside the well, the potential value was V = -10?
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Transcribed Image Text:A particle is trapped into a potential well centered on the position x = 0, of length R. Inside the
well, the value of the potential is zero. Outside of the well, the potential is infinite.
Draw a schema of the problem, and define all axes you may need to solve the problem
Give the Schrodinger equation of the wave function of that particle, explaining all terms
involved into the equation.
) What are the proper values of the energy of this particle? We will assume that the energy
of the particle is all the time positive, and we will use the quantum number n for the states of
energy.
We will assume we are able to measure the energy of the particle with a given precision.
Show that there is a maximal precision you can obtain.
If you want to be able to measure the difference between two states of energy (i.e. the
difference between two energy levels), your precision needs to be about half of the difference
you are trying to measure. Deduce from the previous question that there is a relation between
n and R in order to be able to measure AE = En+1 — En
-
Would the results be the same if inside the well, the potential value was V = -10?
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