How can the particle fit in the well then?

[touqra]

In an infinite square well potential, the ground state of a particle, has a wavelength twice the length of the well. How can the particle fit in the well then? It's not even one wavelength.

 

[masudr]

When you say the particle['s]...wavelength, I think you mean the wavelength of the particle's wavefunction. Please understand the fundamental difference between the two things.

The wavefunction of the particle is (at the very least) a mathematical object representing all we can know about the state the particle is in. To determine other properties of the particle, you must perform measurements of dynamical variables of the system.

 

[gulsen]

The wavefunction describes the probability of finding a particle in a given interval, the particle is usually considered to be a point particle. Eh, at least in the problems I've worked out so far.

 

[jtbell]

In an infinite square well potential, the ground state of a particle, has a wavelength twice the length of the well. How can the particle fit in the well then? It's not even one wavelength.

The wave function is zero in the middle of each full wavelength, which matches the value it must have outside the box.

If you have a classical vibrating string with fixed ends, the fundamental mode of vibration (the one with lowest frequency) has a wavelength that is twice the length of the string, for exactly the same reason.

If you're thinking that the wavelength has to do with particle size, and you can't have half a particle, therefore you can't have half a wavelength, that's not so.