𝛹2(x,t) are two solutions of the equation of Schrödinger
for a particular potential V(x,t), show that the linear combination
arbitrary 𝛹(x,t) = c1𝛹1(x,t) +
c2𝛹2(x,t) is also a solution of this
equation. Or That is, which solutions of the Schrödinger equation
obey the principle of superposition.
2 - ) At a certain instant, a wave function depends
on position as shown in the figure below.
(a) If a measurement were made that could locate the associated
particle in a dx element of the x axis at that instant, where it
would be greater the probability of finding it?
(b) Where would this probability be lowest?
(c) The odds that it will be found at any positive x-axis value
would be greater than the chances that it will be found at any
negative value?
- 1 (9.82 KiB) Viewed 43 times
“one-dimensional” box of length a, given below, to calculate the
probability that, in a measured, the particle is found within a
region measuring a/3, considered from the far right of the box. The
particle is in its state of lower energy. Compare with the
probability that would be predicted classically.
𝛹(x,t) = (2/a)1/2 cos (px/a)
e-iEt/h , -a/2 < x < a/2
𝛹(x,t) = 0 , x ≤ -a/2 ou x ≥ a/2
4 - ) The wave function from the previous exercise
satisfies the Shrödinger equation, provided that E =
π2h2/2ma2. Use it to
estimate the total energy of a neutron, from mass of about
10-27 kg, when we assume that it moves freely in the
inside a core with linear dimensions of approximately
10-14 m, but which is strictly confined to the core.
Express the estimate in MeV. Is it over there will be close to the
real energy of a neutron in the lowest energy state of a typical
core.
5 - )
𝛹(x,t) = Asen(2πx/a) e-iEt/h, -a/2 <
x < a/2
𝛹(x,t) = 0 , x ≤ -a/2 ou x ≥ a/2
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adjusting the value of the constant multiplicative A so that the
total probability of finding the particle associated at some point
in the region of length a is 1.
(b) Compare with the value of A = (a/2)1/2 from
exercise 3. Discuss the comparison.
(xt) 5 I fixo I +1x -5 0 5 10
(x, t) t fixo A -a/2 0 a12