Bound States of Infinite Square Well

In summary, a bound state in an infinite square well is a confined quantum mechanical state with limited range of motion. Its energy is determined by the size of the well and the mass of the particle, calculated using the Schrödinger equation. The infinite square well potential is a useful model for studying quantum systems and demonstrates concepts such as energy quantization and wave function behavior. The energy of a particle in an infinite square well is quantized and inversely proportional to the size of the well.
  • #1
"pi"mp
129
1
Hi all,
So I was recently set straight on the fact that bound state does *not* necessarily mean E<0 but rather is the statement that E<V(+/- infinity). So how do we apply this definition to the infinite square well where the potential at +/- infinity vanishes, and yet the bound states have positive energy?
Thanks in advance!
 
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  • #2
The potential of the infinite square well at infinity is infinity?
 
  • #3
oh god, yes of course. I was confusing it with the w.f. vanishing. Was very tired when i posted! thx
 

1. What is a bound state in an infinite square well?

A bound state in an infinite square well is a quantum mechanical state in which a particle is confined to a finite region by potential barriers on either side. In other words, the particle has a limited range of motion and cannot escape the well.

2. How is the energy of a bound state in an infinite square well determined?

The energy of a bound state in an infinite square well is determined by the size of the well and the mass of the particle. It can be calculated using the Schrödinger equation, which describes the behavior of quantum systems.

3. What is the significance of the infinite square well potential in quantum mechanics?

The infinite square well potential is a simple model that is used to study the behavior of quantum systems. It allows for the exploration of important concepts such as energy quantization and wave function behavior in a confined space.

4. Can a particle in an infinite square well have any energy value?

No, the energy of a particle in an infinite square well is quantized, meaning it can only have certain discrete values. This is a fundamental aspect of quantum mechanics and is a result of the particle being confined within the potential well.

5. How does the size of the infinite square well affect the energy of a bound state?

The energy of a bound state in an infinite square well is inversely proportional to the size of the well. This means that as the size of the well increases, the energy of the bound state decreases. This relationship can be seen in the quantized energy levels of the particle in the well.

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