Bound State Condition: Definition Explained

In summary, the bound state condition is when the energy is less than 0 and the wavefunction decays to 0 as r approaches infinity. However, there is disagreement about whether this definition is precise enough and whether other factors should be considered, such as the type of potential well and the behavior of the wavefunction at infinity. It is also noted that not all wavefunctions that decay to 0 at infinity are considered bound states, as there are exceptions such as finite wells and attractive delta functions.
  • #1
OB1
25
0
What is the precise definition of the bound state condition? Thanks in advance.
 
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  • #2
E < 0 and that the wavefunction "decays" to 0 as r-> infty
 
  • #3
malawi_glenn said:
E < 0 and that the wavefunction "decays" to 0 as r-> infty
Disagree with you, though I'm not insisting. Consider a harmonic oscillator: all energies > 0, still bound states. Wave function should "decay" at infinity, but something must be said about when it decays: e.g. a moving Gaussian wave packet decays faster than an exponent, but does not correspond to a bound state.
 
  • #4
Well, a harmonic oscillator is bound by definition though. It's in an infinite potential well.

If it wasn't an infinite potential well, the particle could tunnel out sooner or later. So it wouldn't be bound then.
 
  • #5
Yes, "If it wasn't an infinite potential well, the particle could tunnel out sooner or later. So it wouldn't be bound then".
 
  • #6
Doesn't any allowed wave function decay to zero at infinity as part of the L2 condition? But not all wave functions are bound states, and we do have bound states in finite wells or attractive delta functions, so the bound state condition can't be just that.
Or am I missing the point, maybe?
 

Related to Bound State Condition: Definition Explained

What is the definition of Bound State Condition?

The Bound State Condition refers to a quantum mechanical phenomenon in which two or more particles are bound together and have a finite amount of energy within a specific region of space. This condition is also known as the quantum confinement effect.

What is an example of the Bound State Condition?

An example of the Bound State Condition is the formation of a hydrogen atom, where an electron is bound to a proton due to their opposite charges. The electron is confined to a specific energy level around the proton, resulting in a stable bound state.

How does the Bound State Condition differ from the Free State Condition?

The Bound State Condition and Free State Condition are two different quantum mechanical states. In the Bound State Condition, particles are confined and have a finite amount of energy, while in the Free State Condition, particles are not confined and can have any energy level.

What are the implications of the Bound State Condition in physics?

The Bound State Condition has many implications in physics, including the stability of atoms and molecules, the behavior of particles in a potential well, and the formation of nuclear and atomic bonds. It also plays a crucial role in understanding the behavior of matter at the quantum level.

Can the Bound State Condition be observed in everyday life?

Yes, the Bound State Condition can be observed in everyday life. Some examples include the stability of atoms and molecules, which allows for the existence of matter as we know it, and the formation of chemical bonds, which are essential for various processes in our daily lives.

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