Energy and Excited States in Semi-Infinite-Well Potential

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In summary, in this conversation, the participants are discussing how to use the semi-infinite-well potential to model a deuteron, a nucleus consisting of a neutron and a proton. The well width is given as 3.5*10-15 m and the potential energy is -2.2 MeV. The main focus is on determining the energy E (in MeV) and the number of excited states for the deuteron. The participants also discuss the formula for calculating the energy of excited states and how to determine when to stop using it. Additionally, they consider the significance of the 2.2 MeV potential energy and its relation to the energy of the deuteron.
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j2dabizo
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Homework Statement



Use the semi-infinite-well potential to model a deuteron, a nucleus consisting of a neutron and a proton. Let the well width be 3.5*10-15 m and Vo -(minus) E = 2.2 MeV. Determine the energy E (in MeV).

How many excited states are there? 0 1 2 3 4 5

What are their energies? (If an excited state doesn't exist, enter a value of zero.)
1st-
2nd-
3rd-
4th-
5th-


Homework Equations





The Attempt at a Solution



I assume that the ground state of the deuteron (n=1) is the E, is this correct in my thinking?

So after you find out the K value for the deuteron with L=width of the well, you use that k value to find out the E(n=1) ground state (which will be the energy we are looking for in part 1), is this correct as well?

As far as the excited states go...how do I determine when we stop using the formula En=n^2...(forgot the rest the book isn't in front of me). We can keep gooing on and on with multipule excited states.

When do we know the threshold...does it have to do with the 2.2 MeV Vo being greater than the E??
 
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Please explain the whole process of finding the energy E (in MeV) and the excited states.Thanks for your help!!
 

Related to Energy and Excited States in Semi-Infinite-Well Potential

What is a semi-infinite-well potential?

A semi-infinite-well potential is a type of potential energy function used in quantum mechanics to describe the behavior of a particle in a confined space. It consists of a finite well on one side and an infinitely high potential barrier on the other side.

What is the significance of a semi-infinite-well potential?

Semi-infinite-well potentials are commonly used to model various physical systems, such as electron behavior in atoms, and to study quantum phenomena, such as tunneling and bound states.

How is the wave function affected by a semi-infinite-well potential?

The wave function of a particle in a semi-infinite-well potential is constrained to the finite well region and must satisfy boundary conditions at the potential barrier. This results in quantized energy levels and a discrete spectrum for the particle's energy.

What is the difference between a finite well and a semi-infinite-well potential?

A finite well potential has finite boundaries on both sides, while a semi-infinite-well potential has one finite boundary and one infinitely high potential barrier. This difference can lead to different behaviors and energy levels for the particle in the two types of potentials.

How is the behavior of a particle in a semi-infinite-well potential affected by the height and width of the potential barrier?

The height and width of the potential barrier can greatly influence the behavior of a particle in a semi-infinite-well potential. A higher and wider barrier can restrict the movement of the particle, while a lower and narrower barrier may allow for more freedom of movement.

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