Sketching ψ(x) for 1-D TISE in Ground State: Potential, Energy, and Behavior

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In summary, the particle is in its ground state and moves in one dimension in a potential with energy E shown on the graph. The equation for ψ is ψ''+2m(E-V0)/ħ^2 ψ=0. For E>V0, ψ goes towards the x axis and ψ and ψ'' have opposite signs. For E<V0, ψ goes away from the x axis and ψ and ψ'' have the same signs. The graph of ψ must end up going towards zero on both ends. The sketch can be done separately for each well and does not need to be exact.
  • #1
Caulfield
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Homework Statement



Particle moves in one dimension in the potential shown here. The energy E is shown on the graph and the particle is in its ground state.
Sketch ψ(x)

Homework Equations



ψ''+2m(E-V0)/ħ^2 ψ=0

The Attempt at a Solution



For E>V0: The graph of ψ goes toward x axis, ψ and ψ'' have opposite signs.

For E<V0: The graph of ψ goes from x axis, ψ and ψ'' have the same signs.

The graph must end up going towards the zero on both ends.
 
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  • #2
You can do it for each well separately right?
It's just a sketch - you you don't need to be exact - so just sum what you get for each one apart.
 

1. What is ψ(x) in the context of the 1-D TISE?

ψ(x) represents the wave function in the one-dimensional Time-Independent Schrodinger Equation (TISE). It describes the probability amplitude of finding a particle at a certain position x in a given potential.

2. What is the potential in the ground state of the 1-D TISE?

The potential in the ground state of the 1-D TISE is the lowest energy state of a particle in a one-dimensional potential well. It is typically a well-defined potential energy function, such as a harmonic oscillator or a square well potential.

3. How is energy related to ψ(x) in the ground state of the 1-D TISE?

In the ground state of the 1-D TISE, the energy of a particle is the minimum possible energy it can have in a given potential. This energy is directly related to the shape and behavior of the wave function ψ(x).

4. What is the behavior of ψ(x) in the ground state of the 1-D TISE?

The behavior of ψ(x) in the ground state of the 1-D TISE depends on the specific potential in which the particle is confined. In general, the wave function will have a finite amplitude within the potential well and will approach zero as it reaches the boundaries of the well.

5. How can I sketch ψ(x) for the ground state of the 1-D TISE?

To sketch ψ(x) for the ground state of the 1-D TISE, you can plot the wave function as a function of position x on a graph. The shape and behavior of ψ(x) will depend on the specific potential in which the particle is confined. It is important to follow the general guidelines for sketching wave functions, such as ensuring that the function is continuous and normalized.

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