Chapter 35: Problem 8
What did Einstein mean by his remark, loosely paraphrased, that "God does not play dice"?
Chapter 35: Problem 8
What did Einstein mean by his remark, loosely paraphrased, that "God does not play dice"?
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Get started for freeWhat's the quantum number for a particle in an infinite square well if the particle's energy is 25 times the ground-state energy?
What's the probability of finding a particle in the central \(80 \%\) of an infinite square well, assuming it's in the ground state?
Find an expression for the normalization constant \(A\) for the wave function given by \(\psi=0\) for \(|x|>b\) and \(\psi=A\left(b^{2}-x^{2}\right)\) for \(-b \leq x \leq b.\)
Is quantization significant for macro molecules confined to biological cells? To find out, consider a protein of mass 250,000 u confined to a \(10 \mu \mathrm{m}\) -diameter cell. Treating this as a particle in a one-dimensional square well, find the energy difference between the ground state and the first excited state. Given that biochemical reactions typically involve energies on the order of \(1 \mathrm{eV}\), what do you conclude about the role of quantization?
A particle is in the \(n\) th quantum state of an infinite square well. (a) Show that the probability of finding it in the left-hand quarter of the well is $$ P=\frac{1}{4}-\frac{\sin (n \pi / 2)}{2 n \pi} $$ (b) Show that for odd \(n\), the probability approaches the classical value \(\frac{1}{4}\) as \(n \rightarrow \infty\)
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