TY - JOUR

T1 - Phase-modulus relations for a reflected particle

AU - Yahalom, A.

AU - Englman, R.

PY - 2003/9/18

Y1 - 2003/9/18

N2 - We formulate analytically the reflection of a one-dimensional, expanding free wave packet (wp) from an infinite barrier. Three types of wp's are considered, representing an electron, a molecule, and a classical object. We derive a threshold criterion for the values of the dynamic parameters so that reciprocal (Kramers-Kronig) relations hold in the time domain between the log-modulus of the wp and the (analytic part of its) phase acquired during the reflection. For an electron, in a typical case, the relations are shown to be satisfied. For a molecule the modulus-phase relations take a more complicated form, including the so-called Blaschke term. For a classical particle characterized by a large mean momentum {K ≫ ℏ[trajectory length/(size of wave packet)2] > > > ℏ/size of wave packet}, the rate of acquisition of the relative phase between different wp components is enormous (for a bullet it is typically 1014 GHz) with also a very large value for the phase maximum.

AB - We formulate analytically the reflection of a one-dimensional, expanding free wave packet (wp) from an infinite barrier. Three types of wp's are considered, representing an electron, a molecule, and a classical object. We derive a threshold criterion for the values of the dynamic parameters so that reciprocal (Kramers-Kronig) relations hold in the time domain between the log-modulus of the wp and the (analytic part of its) phase acquired during the reflection. For an electron, in a typical case, the relations are shown to be satisfied. For a molecule the modulus-phase relations take a more complicated form, including the so-called Blaschke term. For a classical particle characterized by a large mean momentum {K ≫ ℏ[trajectory length/(size of wave packet)2] > > > ℏ/size of wave packet}, the rate of acquisition of the relative phase between different wp components is enormous (for a bullet it is typically 1014 GHz) with also a very large value for the phase maximum.

UR - http://www.scopus.com/inward/record.url?scp=0141570794&partnerID=8YFLogxK

U2 - 10.1021/jp034185i

DO - 10.1021/jp034185i

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AN - SCOPUS:0141570794

SN - 1089-5639

VL - 107

SP - 7170

EP - 7174

JO - Journal of Physical Chemistry A

JF - Journal of Physical Chemistry A

IS - 37

ER -