Infinity & Limits: Why Does Energy Not Become Infinite?

  • Context: Undergrad 
  • Thread starter Thread starter dyn
  • Start date Start date
  • Tags Tags
    Infinity Limits
Click For Summary

Discussion Overview

The discussion revolves around the concept of energy levels in quantum mechanics, specifically in relation to infinite systems such as an infinite potential well and a harmonic oscillator. Participants explore why energy does not become infinite despite the presence of infinite energy levels, examining the implications of limits and infinity in this context.

Discussion Character

  • Exploratory, Conceptual clarification, Debate/contested

Main Points Raised

  • One participant expresses confusion about why energy does not become infinite in systems with infinite energy levels, such as the infinite well and harmonic oscillator.
  • Another participant questions the strength of the reference to being told that energy does not become infinite, suggesting that energy levels can theoretically exceed any value without a limit.
  • A different participant notes that while there is an infinite number of integers, each integer is finite, implying a distinction between the concept of infinity and finite values.
  • A follow-up question seeks clarification on whether energy, which varies as n² or n, ever actually reaches infinity.
  • One participant asserts that every energy level has a finite energy, prompting further inquiry into the meaning of "it" in the context of energy levels.

Areas of Agreement / Disagreement

Participants do not reach a consensus on the nature of energy levels and infinity, with multiple competing views presented regarding the interpretation of infinite energy levels and their implications.

Contextual Notes

The discussion includes assumptions about the nature of energy levels and infinity, but these assumptions are not explicitly defined or resolved, leaving room for interpretation and further exploration.

dyn
Messages
774
Reaction score
63
Hi
I'm confused about something from quantum mechanics but it concerns infinity and limits.
For an infinite well the energy levels vary as n2 and for an harmonic oscillator the energy levels vary as n with n taking integer values in both cases with no upper bound.
In both cases there are infinite levels but I have been told the energy does not become infinite in either case.Why does the energy not become infinite ?
Thanks
 
Physics news on Phys.org
'Have been told' isn't a very strong reference ...
Energy levels can exceed any value, as you say: no upper bound. Anything to disallow that ?

Besides the given that the energy supply of the universe is probably finite, I see no limit for this theoretical case.
 
There is an infinite number of integers, but every integer is finite. Same thing.
 
let me re-phrase my question. If the energy varies as n2 or n , does it ever become infinite ?
 
What is "it"?
Every energy level has a finite energy.
 
  • Like
Likes   Reactions: dyn

Similar threads

Undergrad Simplifying limit with Stirling approximation
  • · Replies 9 ·
Replies
9
Views
3K
Undergrad Infinite value of amplìtude of an undamped driven oscillator at resonance
  • · Replies 18 ·
Replies
18
Views
3K
Undergrad Does potential energy curve spacetime?
  • · Replies 28 ·
Replies
28
Views
2K
Undergrad Can anyone justify this derivation of Stirling’s approximation?
  • · Replies 19 ·
Replies
19
Views
4K
Undergrad Understanding No Energy Degeneracy in Sakurai's Quantum Mechanics
  • · Replies 2 ·
Replies
2
Views
3K
Undergrad Boltzmann brains and limitless energy....
  • · Replies 15 ·
Replies
15
Views
3K
Graduate Does there exist a proof for these conjectures?
  • · Replies 2 ·
Replies
2
Views
2K
Undergrad Does the concept of infinite parallel universes justify absurdities?
  • · Replies 4 ·
Replies
4
Views
2K
Undergrad In which sense(s) do square integrable functions go to zero at infinity?
  • · Replies 2 ·
Replies
2
Views
3K
Graduate Rudin 2.41, why does an unbounded infinite set have no limit points?
  • · Replies 3 ·
Replies
3
Views
9K