Energy spectrum from a hamiltonian

In summary, the energy spectrum from a Hamiltonian is the set of all possible energy states that a system can take on. It is directly related to a system's behavior and can be influenced by factors such as physical properties, external forces, and interactions with other systems. The energy spectrum is calculated by solving the Schrödinger equation and can change over time depending on the system's dynamics and external influences.
  • #1
Fixxxer125
41
0
Hi there, just wondered if anyone could help me...
If I am given a hamiltonian describing a particle in one dimension

H=p^2/2m +1/2 (γ(x-a)^1/2) + K(x-b) how do I go about finding the eigenstates and eigenvalues of this hamiltonian?
Many thanks
 
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  • #2
For that classical Hamiltonian, can you think of a canonical transformation in phase space to get rid of the square root ?
 

FAQ: Energy spectrum from a hamiltonian

What is the energy spectrum from a Hamiltonian?

The energy spectrum from a Hamiltonian refers to the set of all possible energy states that a system can take on based on its Hamiltonian, which is a mathematical operator that describes the system's energy.

How is the energy spectrum related to a system's behavior?

The energy spectrum is directly related to a system's behavior as it determines the possible energy levels that the system can possess. This, in turn, affects how the system will behave and evolve over time.

What factors can influence the energy spectrum of a system?

The energy spectrum of a system can be influenced by various factors such as the system's physical properties, external forces, and interactions with other systems. Additionally, the shape of the Hamiltonian and the type of potential energy also play a role in determining the energy spectrum.

How is the energy spectrum calculated?

The energy spectrum is calculated by solving the Schrödinger equation, which is a mathematical equation that describes the behavior of quantum systems. This equation takes into account the Hamiltonian and other relevant parameters to determine the possible energy states of the system.

Can the energy spectrum change over time?

Yes, the energy spectrum of a system can change over time depending on the system's dynamics and any external influences. For example, if the Hamiltonian changes, the energy spectrum will also change accordingly.

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