Relativistic Center of Mass System

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Relativistic Center of Mass System
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• The energy available for inelastic processes is

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The Bohr model

• Energy was quantized
• Angular Momentum was quantized

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Bohrs argument
Assume nucleus infinitely heavy Assume electron
is moving in circular orbit of radius,r,with
speed v then
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Bohr assumed that the orbital angular momentum
was quantized i.e. Consequently we obtain
fixed values of
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For Hydrogen Z1
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Axiomatic approach to the formulation of Quantum
Mechanics

• We assume there exists a function
• Which contains all the information about a system
  at time,t. We shall say that is the
  state of the system

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Axiom

• It is impossible to measure all the properties of
  a physical system simultaneously
• Example and

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• The classical observable are related to linear
  operators acting which act on the wave functions
  to give eigenvalues which are the possible
  results of measurement
• If the system is such that we know exactly what
  the value of an observable is then it is in an
  eigenstate ?n and the result of measurement will
  necessarily give us the associated eigenvalue

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Classical Observables?Operators
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• Results of measurements are eigenvalues of
  operators
• ?(r,t) represents a probability wave
• Satisfies the Schrödinger equation
• Wave function a sum(principle of superposition of
  states) over all possible
• eigenstates

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• Bound state problem

Eigenstate-solution of TISE Corresponding to
eigenvalue En
cn2 probability of getting value En
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Continuum Problem
Probability density
Probability current
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Lemma A potential is st V(-x)V(x) then assume
that for a given E the wave function is not
degenerate then these functions must have have a
definite parity



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Example
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• Eigenfunctions are orthogonal
• Can project our value of cq

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Continuity

• ?satisfies a second order differential equation
  in (x,y,z)
• And if V is any kind of ordinary function we must
  have
• ?(?) to be continuous and have continuous first
  derivative

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Particle in a box
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Boundary Conditions
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