Triggering a Transition Between Quantum States

In summary, the conversation discusses a particle in an infinite square well with an initial wave that is a superposition of the ground state and first excited states. The value C=1/2 is shown to normalize the wave if the two states are already normalized. The wave function at any later time is found and it is shown that the superposition state is not stationary, but the average energy of the state is equal to the arithmetic mean of the ground state energy and the first excited state energy.
  • #1
vs667290
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Consider a particle in an infinite square well described initially by a wave that is superposition of the ground state and the first excited states of the well: Ψ(x,t = 0) = C[ψ1(x) +ψ 2 (x)]
(a) show that the value C =1/ 2 normalizes this wave, assuming 1 ψ and 2 ψ are themselves normalized.
(b)find Ψ(x,t) at any later time t.
(c) show that the superposition state is not a stationary state, but that the average energy of this state is the arithmetic mean (E1+E2)/2 of the ground state energy E1 and the first excited state energy E2.
 
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  • #2
Hi vs667290, welcome to PF. Please use the template for homework help, show us the relevant equations and your approach to the problem before asking for help.
 

What is a quantum state?

A quantum state is a mathematical description of the state of a quantum system. It includes all the information about the system, such as its position, momentum, and other physical properties.

What does it mean to trigger a transition between quantum states?

Triggering a transition between quantum states means causing a change in the quantum state of a system. This can be done by applying an external force or by measuring the system, which causes it to collapse into a different state.

Can quantum states be controlled?

Yes, quantum states can be controlled by manipulating the system through various techniques such as applying electromagnetic fields or using quantum gates. However, the exact control that can be achieved depends on the specific system and its environment.

What are the practical applications of triggering transitions between quantum states?

Triggering transitions between quantum states is an essential aspect of quantum computing, where it is used for information processing and storage. It also has applications in quantum communication, cryptography, and sensing.

Are there any limitations to triggering transitions between quantum states?

Yes, there are limitations to triggering transitions between quantum states. One of the main limitations is the fragility of quantum systems, which can easily be disturbed by external factors, leading to errors in the transition process. Additionally, the exact control of quantum states is challenging to achieve, making it difficult to perform precise manipulations.

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