Consider a free particle of mass m in one dimension.
Consider a free particle of mass m in one dimension.
Calculate it's propagator in momentum space:.This propagator is the probability amplitude for a system originally prepared to be in state | Pa> at t=ta to be found in state | Pb> at a later time t=tb.
Calculate it's propagator in momentum space:.This propagator is the probability amplitude for a system originally prepared to be in state | Pa> at t=ta to be found in state | Pb> at a later time t=tb.
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|a,t>=exp[(-iH(t-t0))/h] |a,t0>
we defined K(p'',t;p',t0) satisfying φ(p'',t)=∫dp' {Kφ(p',t0)} //φ(p'',t):=
we can show:K= is a eigenfunction of Hamiltonian which means it can be a stationary state.
and the position of that state should have infinete uncertainly accounting for uncertainly principle.
we defined K(p'',t;p',t0) satisfying φ(p'',t)=∫dp' {Kφ(p',t0)} //φ(p'',t):=
we can show:K= is a eigenfunction of Hamiltonian which means it can be a stationary state.
and the position of that state should have infinete uncertainly accounting for uncertainly principle.
1年前
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