Poschl-Teller potential

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In summary, the Poschl-Teller potential is a mathematical function used in quantum mechanics to describe the behavior of a particle bound by a central force field. Its formula is V(r) = -A/(1-e^(-2αr))^2, where V(r) is the potential energy, A is a constant related to the depth of the potential well, and α is a constant related to the width of the potential well. Its main applications include modeling bound states and studying particle scattering, but it has limitations such as not accounting for quantum tunneling or particle interactions. It is a generalization of the Morse potential and related to the Coulomb potential, with each potential having its own strengths and limitations.
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t_n_p
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Homework Statement



http://img125.imageshack.us/img125/2923/85098487ch9.jpg

The Attempt at a Solution



Because there is no wavefunction specified, is it sufficient to show A+A- = (ε+1) and hence perform the expansion [(-d/dx)+tanh(x)][(d/dx)+tanh(x)]?
 
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whoops, can mods move to advance physics forum
 
  • #3
You should solve the differential equation, you'll see that \Phi goes as Exp[-ikx](tanh x + ik) + Exp[i k x] (tanh x - ik )
 

What is the Poschl-Teller potential?

The Poschl-Teller potential is a mathematical function that is frequently used in quantum mechanics to describe the behavior of a particle bound by a central force field. It is named after its creators, physicists Karl Pöschl and Eduard Teller.

What is the formula for the Poschl-Teller potential?

The formula for the Poschl-Teller potential is V(r) = -A/(1-e^(-2αr))^2, where V(r) is the potential energy as a function of distance r, A is a constant related to the depth of the potential well, and α is a constant related to the width of the potential well.

What are the applications of the Poschl-Teller potential?

The Poschl-Teller potential is commonly used in quantum mechanics to model the behavior of a particle in a bound state, such as an electron in an atom or a particle in a potential well. It can also be used to study the scattering of particles by a potential barrier.

What are the limitations of the Poschl-Teller potential?

The Poschl-Teller potential is a simplified model that does not take into account the effects of quantum tunneling or the interaction of particles with each other. It is also limited to spherically symmetric potentials and cannot be applied to more complex systems.

How does the Poschl-Teller potential compare to other potential models?

The Poschl-Teller potential is a generalization of the Morse potential, which is another commonly used model in quantum mechanics. It is also related to the Coulomb potential, which describes the interaction between charged particles. Each potential has its own strengths and limitations, and the choice of which to use depends on the specific system being studied.

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