Quantum Mechanics: Discrete Energy Changes Explained

[roshan2004]

According to quantum mechanics,the energy changes are not continuous but discrete. What does it really means?

 

[thebigstar25]

the fact that the energy is discrete means that it can only has certain values ..

its true that quantum mechanics says so, but it not always the case .. in fact the idea of quantization was posted by Planck to fit expermintal results ..

having discrete energy values can occur only with certain conditions .. I am not really expert in this field but i think that the other members will help u more in your question..

 

[roshan2004]

I am sorry,but I still could not get it

 

[thebigstar25]

mmm, well .. in quantum mechanics when the energy changes say from state1 to state2 (when its excited) let's take the example of harmonic oscillator , in state1 it has an energy of 0.5h-par w and in state2 it has 3/2 h-par w , so in this case quantum mechanics states that it can't have an energy between these values(say 0.8 h-par w) ..

I hope this answers your question, if not please clarify your question more..

 

[roshan2004]

and the continuous energy change means!

 

[thebigstar25]

it simply means that the energy is allowed to have any value with no restrictions .. I can't just talk about this topic in general its just sooo wide to discuss .. if u have any specific examples u want to check on u can post them here .. continuos or discerte energy depends on what problem u have ..

 

[ZapperZ]

According to quantum mechanics,the energy changes are not continuous but discrete. What does it really means?

Where did QM say such a thing?

Note that these things depends very much on the SITUATION. For example, you can get discrete energy change in, say, atomic spectrum, but you get a CONTINUOUS energy change in the conduction band of a metal. Look at the energy of photoelectrons, for example, in a typical photoelectric effect. The spectrum of energy attained by these electrons has a continuous distribution. It isn't discrete.

Want more example? Use a spectrometer and look at the spectrum from a gas in a discharge tube, versus the spectrum from an incandescent light bulb. The latter gives you a continuous spectrum.

Yet, ALL of these systems can be described by QM, meaning that QM can produce both continuous and discrete energy description. It depends on the conditions, especially the BOUNDARY CONDITION of these systems (solve the Schrodinger equation for a free particle).

Zz.

 

[roshan2004]

Thanks,since I am just beginning to learn this lesson.

 

[thebigstar25]

I can understand your feeling , u have many questions in mind and u just want to know all the answers .. my advice to u not to rush and take it step by step .. if u have time and u really want to understand this subject read the history of quantum this would help u more than u think ..

all the best with your studies..

 

[roshan2004]

Is it right then that's why the spectrum of Hydrogen is discrete not continuous because of the energy change in hydrogen is not continuous.

 

[thebigstar25]

its logical to say so .. u know that the energy is related to the frequency so if the energy is discrete that means that the frequencies would have certain values so it will result in the spectrum .. and i think Zapperz agrees with what i just said ..

 

[akhmeteli]

According to quantum mechanics,the energy changes are not continuous but discrete. What does it really means?

I guess several answers to your question can be given, reducing the problem to something more primitive, but eventually the explanation cannot go deeper than the level of axioms of the theory. So I'd say discrete energy changes are a mathematical consequence of some approximate quantum theories, such as those described by the Shroedinger or Dirac equation, although for all systems discrete energy changes (if they exist at all) coexist with continuous ones. Furthermore, in more precise theories, such as quantum electrodynamics, strictly speaking, there are no discrete energy changes because of the so called natural line width.

Qualitatively, the idea of discrete energy changes has a very close classical analogy: a guitar string (in an ideal case) can produce sound with a discrete acoustical spectrum: the fundamental frequency and obertones.

 

[eaglelake]

According to quantum mechanics,the energy changes are not continuous but discrete. What does it really means?

This is not true, as others have pointed out.

In general, free particles have a continuous spectrum of energy eigenvalues, while bound particles have a discrete energy spectrum.

Thus, the energy of a free particle can change by an infinitesimally small amount. But, a particle in a bound state can change only by discrete amounts.