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Mean position of a parti le submitted to a potential barrier D. Mer ier, V. Régnier ? Abstra t A one-dimensional Klein-Gordon problem, whi h is a physi al model for a quantum parti le submitted to a potential barrier, is studied numeri ally : using a variational formulation and a Newmark numeri al method, we ompute the mean position and standard deviation of the parti le as well as their time evolution. Key words Klein-Gordon equation, Newmark method, mean and standard devia- tion, kernel smoothing, linear regression. AMS 35A15, 65M06, 65M12, 81Q05, 81Q10. 1 Introdu tion It has been well-known for a few years now that in quantum me hani s a parti le an limb up a step even if it has not enough energy a priori and it will be ree ted then with a delay. In lassi al me hani s it would just try and go ba k to its position. Everything happens here as if the parti le ould go through a wall ( f. Fig. 5.1 in [17?) ! This phenomenon is alled tunnel ee t and has been a subje t of interest for physi ians and mathemati ians : the delay has been measured by the physi ists A.

iennes

tion

initial boundary

tly supported initial

exa tly

gaussian wave

tral theory

mer ieruniv-valen

delay whi

numeri al

Voir

Publié par

pefav

Nombre de lectures

Langue

English

Mehmeti maths

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35A15,
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:
to
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of
thank
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for
solution
so.
at
quan
time

t
ne

Voir

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