Free Particle & Square Well Potential Explained

[kaadshah123456]

free particle can be thought of as unbound particle
and what about square well potential with finite walls? coz it has both bound and unbound states

please help m confused thanks in advance

 

[bhobba]

By definition a free particle is a particle that acts as if its the only thing in an inertial frame.

An inertial frame is defined as a frame where all points are the same, all directions are the same, and all instances in time are the same. Without going into the details (you will find it in Landau - Mechanics) that constrains its Lagrangian to be mv^2/2 so the particle moves at a constant velocity. The Hamiltonian is then the same but its more usual to write it as p^2/2m.

You shove that into Schrodinger's equation and you get the wave solution:
http://www.physics.ox.ac.uk/Users/smithb/website/coursenotes/qi/QILectureNotes3.pdf

You place a particle in a square well potential and its no longer in an inertial frame (all points are no longer the same) - the Hamiltonian is different and you get different solutions to Schroedinger's equation.

Thanks
Bill

 

[kaadshah123456]

By definition a free particle is a particle that acts as if its the only thing in an inertial frame.

An inertial frame is defined as a frame where all points are the same, all directions are the same, and all instances in time are the same. Without going into the details (you will find it in Landau - Mechanics) that constrains its Lagrangian to be mv^2/2 so the particle moves at a constant velocity. The Hamiltonian is then the same but its more usual to write it as p^2/2m.

You shove that into Schrodinger's equation and you get the wave solution:
http://www.physics.ox.ac.uk/Users/smithb/website/coursenotes/qi/QILectureNotes3.pdf

You place a particle in a square well potential and its no longer in an inertial frame (all points are no longer the same) - the Hamiltonian is different and you get different solutions to Schroedinger's equation.

Thanks
Bill

but can you say that free particle is unbound?? acc to definatioms unbound sysyem are those in which particle can go to infinite

 

[bhobba]

but can you say that free particle is unbound?? acc to definatioms unbound sysyem are those in which particle can go to infinite

That's the same thing as being in an inertial frame. If it can't go to infinity then all points are not the same.

Thanks
Bill

 

[kaadshah123456]

now i und.
thanks lot:)

 

[DrClaude]

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