Transition from bound states to continuous states

In summary, the conversation discusses the possibility of a transition from a bound state to a state with energy greater than 0 in a Hydrogen atom. The individual asking the question has calculated the probability amplitude but it came out as 0, which is in contrast to the known physical possibility of ionizing an atom. The conversation suggests sharing the calculation and making sure to conserve angular momentum in the transition. Ultimately, it was determined that the issue was a calculation mistake.
  • #1
giova7_89
31
0
Transition from bound states to "continuous" states

If I have the Hamiltonian for the Hydrogen atom and a perturbation given by a classical electric field (the kind of problems you get in an ordinary course about QM, no QFT involved), can I have a transition from a bound state (I intend a discrete state [tex]|n,l,m>[/tex]) to a state with energy greater than 0 (that is a state in the continuous spectrum of the unperturbed Hamiltonian). I calculated the probability amplitude [tex]<E|n,l,m>_t[/tex] by means of the Dyson series and it comes off as 0...
 
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  • #2


And what bothers me is that I know that is physically possible to ionize an atom... That is, send an electron in a bound state into a scattering state..
 
  • #3


giova7_89 said:
If I have the Hamiltonian for the Hydrogen atom and a perturbation given by a classical electric field (the kind of problems you get in an ordinary course about QM, no QFT involved), can I have a transition from a bound state (I intend a discrete state [tex]|n,l,m>[/tex]) to a state with energy greater than 0 (that is a state in the continuous spectrum of the unperturbed Hamiltonian). I calculated the probability amplitude [tex]<E|n,l,m>_t[/tex] by means of the Dyson series and it comes off as 0...
Maybe you should share your calculation. Otherwise one cannot tell what you did wrong.
 
  • #4


Did you make sure to conserve angular momentum in your transition?
 
  • #5


Thank you but I managed to solve my problem. It was a calculation mistake!
 

1. What is the difference between bound states and continuous states?

Bound states refer to a system in which particles are confined to a specific region or energy level, while continuous states refer to a system in which particles are free to move or exist at any energy level within a given range.

2. How does a system transition from bound states to continuous states?

This transition can occur through various processes, such as increasing the temperature, changing the external conditions, or adding energy to the system.

3. What are some examples of systems that exhibit this transition?

Some examples include the transition of electrons in a solid from bound states to continuous states when heated, the ionization of atoms when exposed to high energy radiation, and the dissociation of molecules into individual atoms at high temperatures.

4. How does the behavior of particles change during this transition?

In bound states, particles are confined and have discrete energy levels, while in continuous states, particles are free to move and have a continuous range of energy levels. This results in changes in the physical properties and behavior of the particles, such as increased mobility and a wider range of interactions.

5. What are the potential applications of understanding this transition?

Understanding the transition from bound states to continuous states is important in various fields, such as material science, chemistry, and astrophysics. It can help us predict and control the behavior of particles in different systems, leading to advancements in technology and the development of new materials and processes.

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