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A PARTICLE OF MASS M MOVESS IN XY PLANE ALONG THE LINE Y=X-4,WITH CONSTANT SPEED V, FIND ANGULAR MOMENTUM OF PARTICLE ABOUT ORIGIN AT ANY INSTANT OF TIME T.

A PARTICLE OF MASS M MOVESS IN XY PLANE ALONG THE LINE Y=X-4,WITH CONSTANT SPEED V, FIND ANGULAR MOMENTUM OF PARTICLE ABOUT ORIGIN AT ANY INSTANT OF TIME T.

Grade:11

1 Answers

Aman Bansal
592 Points
7 years ago

Dear Student,

A free particle is not subjected to any forces, its potential energy is constant.  Set V(r,t)=0, since the origin of the potential energy may be chosen arbitrarily.  The Schroedinger equation then becomes 

 .

Plane waves are possible solutions,

y(r,t)=Aexp(k×r-wt),

as long as  hw=h2k2/(2m).  

We have

,

 

using the de Broglie relations.

A plane wave represents a particle whose probability of presence is constant throughout space;

|y(r,t)|2=|A|2=constant.

 

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