(10) A non-relativisitic particle of mass m moves in a one-dimensional potential well with infinitely hard walls at z = -L and r = +L (in other words, at the walls the potential energy U becomes infinite). In between these walls the potential takes some undetermined form U(2). The total energy of the particle is zero (E = 0). Its wave function is: (z) = K for – L
(10) A non-relativisitic particle of mass m moves in a one-dimensional potential well with infinitely hard walls at z = -L and r = +L (in other words, at the walls the potential energy U becomes infinite). In between these walls the potential takes some undetermined form U(2). The total energy of the particle is zero (E = 0). Its wave function is: (z) = K for – L
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Transcribed Image Text:(10) A non-relativisitic particle of mass m moves in a one-dimensional potential well with
infinitely hard walls at a = -L and æ = +L (in other words, at the walls the potential energy U
becomes infinite). In between these walls the potential takes some undetermined form U(x). The
total energy of the particle is zero (E = 0). Its wave function is:
(z) = K
for – L< x < +L,
where (x) = 0 elsewhere and K is a constant.
(i) Use the Schrödinger equation to determine the potential energy U as a function of a between
the walls, at which z = +L.
(ii) Determine the value of the constant K. A useful integral is: fa"dr = n+1.
(iii) At what value of z is the probability density the greatest for finding this particle? The first
and second derivative tests can be useful, or you could make a graph.
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