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MMLU-Pro / 3642 / A one-particle, one-dimensional system has the state function

Problem

Answer published by the source. Consult the official source to check your work against its answer.

question

A one-particle, one-dimensional system has the state function Ψ=(sinat)(2/πc2)1/4e−x2/c2+(cosat)(32/πc6)1/4xe−x2/c2 \Psi=(\sin a t)\left(2 / \pi c^2\right)^{1 / 4} e^{-x^2 / c^2}+(\cos a t)\left(32 / \pi c^6\right)^{1 / 4} x e^{-x^2 / c^2} where aa is a constant and $c=2.000 Å$. If the particle's position is measured at t=0t=0, estimate the probability that the result will lie between $2.000 Å$ and $2.001 Å$.
Plain-text mathematical notation (without MathML)
A one-particle, one-dimensional system has the state function
Ψ=(sinat)(2/πc²)^(1/4)e^(−x²/c²)+(cosat)(32/πc⁶)^(1/4)xe^(−x²/c²)
where a is a constant and $c=2.000 Å$. If the particle's position is measured at t=0, estimate the probability that the result will lie between $2.000 Å$ and $2.001 Å$.
Original LaTeX notation
A one-particle, one-dimensional system has the state function
$$
\Psi=(\sin a t)\left(2 / \pi c^2\right)^{1 / 4} e^{-x^2 / c^2}+(\cos a t)\left(32 / \pi c^6\right)^{1 / 4} x e^{-x^2 / c^2}
$$
where $a$ is a constant and $c=2.000 Å$. If the particle's position is measured at $t=0$, estimate the probability that the result will lie between $2.000 Å$ and $2.001 Å$.

category

chemistry

options

  1. 0.000189
  2. 0.000350
  3. 0.000500
  4. 0.000265
  5. 0.000075
  6. 0.000312
  7. 0.000540
  8. 0.000216
  9. 0.000426
  10. 0.000127

src

scibench-quan

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Source and history

upstream_id / Original problem ID
3642
task_id
525a70bd-4081-5220-a42b-9c04df44799c
task_key
default--test--3642
task_revision_id
1
config / split
default / test

Official source

initial import