Quantum Mechanics Solution Manual 

© Leon van Dommelen 

3.5.6.3 Solution pipeec
Question:
What is the eigenfunction number, or quantum number, that produces a macroscopic amount of energy, 1 J, for macroscopic values 1 kg and 1 m? With that many energy levels involved, would you see the difference between successive ones?
Answer:
Putting the generic expression for the eigenvalues,
equal to 1 J and plugging in the given numbers:
Solving for , you get 4.268 64 10. Obviously, there is no way to distinguish that many energy levels. A calculator cannot even display all 34 digits of this number, even if you knew to enough digits accuracy to compute 34 digits.