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Potential Wells
The forces of two types appear at interaction of particles ? the long-range repulsive forces and short-range attractive forces. As a result the potential of interaction represents not monotonic function of distance between particles. The region near attracting center, in which the total energy of particle is later than maximum potential energy, is called potential well. According to classic physics for particle can be leaved potential well the additional energy must to be imparted to it. Its value must be equal or grater the difference between height of potential barrier and total particle energy. Contrary to that, in quantum mechanics exist nonzero probability particle to be out of potential well even if its energy is not enough to travel over potential barrier. Such possible levels of particle?s energy are discrete, because particle?s energy later then height of the barrier.
In that model is considered simplest case of one-dimensional rectangular well of finite depth U0. The particle comes flying to barrier from well. The model demonstrates its wave function, but you may chouse radio button |ψ|2 to see the probability of detecting the particle in some region of space (it is proportional to the square of the wave function in that region). With help of the floating bands controls change a mass of particle compare to mass of proton, its energy E, and a depth U0 and a width L of potential well and examine the allowed energies for a particle. Activate check box to observe eigenfunctions for given levels of energy. Compare the conclusions from your observations with the same from observations the ?Particle in a Box? and the ?Potential barriers? activities.
How the allowed energies for a particle confined in a potential well of finite depth correspond to the allowed energies for a particle confined in a potential well of infinite depth?
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