Quantum number and energy levels

  • #1
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how does the quantum number n in the wavefunction equation for a particle in a 1D box lead to increasingly well-separated energy levels?
I know that the separation of energy between the levels is given by ΔE = (2n+1)h^2 / 8mL^2 which means that the higher the n, the greater the energy separation, which explains this mathematically. But I just don't understand the concept behind the idea.
 

Answers and Replies

  • #2
strangerep
Science Advisor
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The... "concept behind the idea"?? :confused:

You need to be clearer on what exactly you don't understand. E.g., do you understand how the ##\Delta E## formula was derived from basic QM principles? Do you understand basic QM principles and math? Or is something else unclear?
 
  • #3
Simon Bridge
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Is that a question you have been asked?

It is the other way around: the restriction to a potential as in the 1D box potential is what leads to well-separated energy levels... it is convenient to number them, which is where the "quantum number" comes from. Basically the energy level equation ##E_n=##.... comes first, and we think, "hey that n makes a handy shorthand for referring to energy levels..."
 

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