Finding the ground state energy of a particle

Schrödinger equation with this boundary condition.In summary, to calculate the ground state energy of a particle with a force acting on it given by U(x) = g*lnx for x>1 and U(x) = ∞ for x = 1, you must use the Schrödinger equation with the boundary condition ψ(x=1) = 0. This will give you the energy eigenvalue for the ground state.
  • #1
sandybeach
2
0
For a particle with a force acting on it whose potential is given by U(x) = g*lnx for x>1 and U(x) = ∞ for x = 1, how do I calculate the ground state energy of the particle?

Supposedly, there is no need to use Schrodinger's equations for this question, which is why I have no idea how to start.

Thanks for any help.
 
Last edited:
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  • #2
You should use the Schrödinger equation; which other ansatz do you have in mind?
 
  • #3
Alright, it must be a mistake then. We were given this question before learning the Schrodinger equation so it was impossible.

Edit: would I just use boundary conditions to solve for E in the time independent schrodinger equation?
 
  • #4
The boundary condition is ψ(x=1) = 0
 

1. What is the ground state energy of a particle?

The ground state energy of a particle is the lowest possible energy state that the particle can have. This is the state in which the particle is most stable and does not require any external energy to maintain its existence.

2. How is the ground state energy of a particle determined?

The ground state energy of a particle is determined by solving the Schrödinger equation, which is a mathematical equation that describes the behavior of quantum particles. The solution to this equation yields the ground state energy of the particle.

3. Why is the ground state energy important in quantum mechanics?

The ground state energy is important in quantum mechanics because it serves as a reference point for all other energy states of a particle. It also provides insight into the stability and behavior of the particle in different environments.

4. Can the ground state energy of a particle ever be zero?

According to the Heisenberg uncertainty principle, it is impossible for a particle to have zero energy. However, the ground state energy can approach zero as the particle approaches absolute zero temperature.

5. What factors can affect the ground state energy of a particle?

The ground state energy of a particle can be influenced by factors such as the particle's mass, its potential energy, and the strength of the forces acting on it. It can also be affected by external factors such as temperature and pressure.

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