*Introduction to Quantum Mechanics*p. 339

**Problem 8.17**About how long would it take for a can of beer at room temperature to topple over spontaneously, as a result of quantum tunneling? Hint: Treat it as a uniform cylinder of mass m, radius R, and length h. As the can tips, let x be the height of the center above its equilibrium position (h/2). The potential energy is mgx, and it topples when x reaches the critical value of x

_{0}= {R

^{2}+ (h/2)

^{2}}

^{1/2}-h/2. Calculate the tunneling probability for E=0. Use the thermal energy ((1/2)mv

^{2}= (1/2)k

_{B}T) to estimate the velocity. Put in reasonable numbers, and give your final answer in years.

The final answer may be found in R.E. Crandall,

*Scientific American*, February 1997, p. 74

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