At the microscopic level, it is possible to understand the spontaneous emission of an alpha particle as having that particle trapped into a potential well, and having it exiting through a tunnel effect. For the following, we will assume we have a potential which is in the following form: ⚫ The potential is symmetrical on the x-axis ⚫ The potential has also a cylindrical symmetry, i.e. in a polar base it does not depend on the polar angle ⚫ For any x =L, the value of the potential is supposed to be Ve**, with A being a positive value. 1) Solve the wave function of the system 2) Assuming you have a probability P to observe the alpha decay, can you write down the equation to compute the values of the coefficients A of the wave functions?
At the microscopic level, it is possible to understand the spontaneous emission of an alpha particle as having that particle trapped into a potential well, and having it exiting through a tunnel effect. For the following, we will assume we have a potential which is in the following form: ⚫ The potential is symmetrical on the x-axis ⚫ The potential has also a cylindrical symmetry, i.e. in a polar base it does not depend on the polar angle ⚫ For any x =L, the value of the potential is supposed to be Ve**, with A being a positive value. 1) Solve the wave function of the system 2) Assuming you have a probability P to observe the alpha decay, can you write down the equation to compute the values of the coefficients A of the wave functions?
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Transcribed Image Text:At the microscopic level, it is possible to understand the spontaneous emission of an alpha
particle as having that particle trapped into a potential well, and having it exiting through a
tunnel effect.
For the following, we will assume we have a potential which is in the following form:
⚫ The potential is symmetrical on the x-axis
⚫ The potential has also a cylindrical symmetry, i.e. in a polar base it does not depend on
the polar angle
⚫ For any x <L, the value of the potential is supposed to be Vo, which is a negative value
• For any x >=L, the value of the potential is supposed to be Ve**, with A being a positive
value.
1) Solve the wave function of the system
2) Assuming you have a probability P to observe the alpha decay, can you write down the
equation to compute the values of the coefficients A of the wave functions?
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