Finding the ground state energy of electron

In summary, the ground state energy of an electron in an infinite 2D circular potential well is lower than that in a square potential well with the same area. The physical significance behind this is that the circular well has a more uniform potential, allowing the electron to move more freely compared to the confined movement in the square well. Similarly, in a 1D infinite square well, as the length decreases, the ground state energy increases due to the increasing potential barrier that the electron must overcome in a smaller region. This is because the ground state energy represents the energy needed for the electron to move from one side of the well to the other.
  • #1
adiputra
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1) The problem is about finding the ground state energy of electron in an infinite 2D circular and square potential well with the same area. I have calculate it via method of separation of variables in polar and cartesian coordinate respectively, and it is found out that the one on the circular well has lower energy(confirm to be correct). But, then the question ask why, as in why is it lower? any physical significance causing that? I heard this is the Uni. Berkeley graduate interview question?

2) Since I am on this question, I remember last time one of my lecturer talking about 1D infinite squae well with length L and I forget what is the physical significance to why as L decrease the ground state energy increase (E=h^2/8mL^2)? If i am not wrong, my lecturer say something like as L decrease, the energy is squeezed into a smaller dimension kind of stuff... but then i don't think it is correct as that reasoning talk about energy density.
 
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  • #2
The physical significance of the ground state energy in a 1D infinite square well is that it represents the energy needed for an electron to move from one side of the well to the other. As the length of the well decreases, the energy required to move from one side to the other increases since the electron is confined to a smaller region and must overcome the increasing potential barrier as it moves through the well. This is why the ground state energy increases as the length of the well decreases.
 

1. What is the ground state energy of an electron?

The ground state energy of an electron is the lowest possible energy level that an electron can occupy in an atom.

2. How is the ground state energy of an electron determined?

The ground state energy of an electron is determined through mathematical calculations and experiments using quantum mechanics principles.

3. Can the ground state energy of an electron change?

No, the ground state energy of an electron is a fixed value for a given atom and cannot be changed without external influence.

4. What is the significance of the ground state energy of an electron?

The ground state energy of an electron helps to define the properties and behavior of an atom, such as its stability and reactivity.

5. How does the ground state energy of an electron relate to electron configurations?

The ground state energy of an electron determines the arrangement of electrons in an atom's electron shells, known as the electron configuration.

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