Stationary states for even parity potential

In summary, the conversation discusses the relationship between stationary states in a system with an even potential energy function and their symmetry. It is asserted that the ground state must be even, not odd, because a state with fewer nodes has lower energy and the ground state typically has no nodes. This is due to the fact that the energy of a state is proportional to the "curvature" of the wavefunction, and the smallest number of nodes a wavefunction can have is zero. Therefore, the ground state must have even symmetry.
  • #1
Nick R
70
0
Hi I know that stationary states in a system with an even potential energy function have to be either even or odd.

Why does the ground state have to be even, and not odd? This is asserted in Griffiths, page 298.
 
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  • #2
Basically, in order for the state to be odd, it has to pass through zero. In order to do this, it needs to change more quickly, which means higher energy. So a state with fewer nodes (places where the wave funtcion goes to zero) always has lower energy than a state with more nodes. Typically the ground state has no nodes, so it can't be odd.
 
  • #3
I suppose it makes sense that stationary states with higher energy have a larger (magnitude of) second spatial derivative on average given the form of the time independent Schrödinger equation.

But that would be true in general. Why would the ground state have an even wavefunction given an even potential?
 
  • #4
As phyzguy said ... the energy of a state is proportional to the "curvature" of the wavefunction (the true mathematical description of curvature is a bit more complicated that just the 2nd derivative, but that simpler version will suffice for this discussion). Thus, states with fewer nodes have lower energies. So you just have to ask youself, what is the smallest number of nodes a wavefunction can have? It's zero, isn't it? So, zero nodes means a wavefunction that doesn't pass through zero, and thus must have even symmetry.
 
  • #5
Errr nevermind let me think about this
 

1. What is a stationary state for even parity potential?

A stationary state for even parity potential is a quantum state of a particle that remains unchanged in time. This means that the probability of finding the particle in this state does not change over time.

2. How is a stationary state for even parity potential different from a non-stationary state?

In a stationary state for even parity potential, the probability of finding the particle in a certain location does not change over time. In contrast, a non-stationary state is constantly changing over time.

3. What determines the energy of a stationary state for even parity potential?

The energy of a stationary state for even parity potential is determined by the potential energy of the system. This potential energy is described by an even parity potential function.

4. Can a particle be in a superposition of stationary states for even parity potential?

Yes, a particle can be in a superposition of stationary states for even parity potential. This means that the particle can exist in multiple states simultaneously and its energy will be a combination of the energies of those states.

5. How are stationary states for even parity potential used in practical applications?

Stationary states for even parity potential are important in understanding the behavior of particles in quantum systems. They can be used to analyze the energy levels of atoms and molecules, and to explain various phenomena in condensed matter physics, such as the behavior of electrons in a crystal lattice.

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