Calculating Energy in a Quantum Chemistry System

In summary, the conversation discusses finding the second lowest value that can be measured for the energy in a system with an initial state of Psi(x) = Ax(b/2 - x) when 0 < x < b/2 and Psi(x) = 0 when b/2 < x < b. The question arises whether to treat the system as a box with width b and possible energy states of E = n^2*h^2/8mb^2 or to use the width b/2. The use of wave equations is also mentioned. The problem is further explained as finding the probability that the measured energy is E2. The correct method of finding Fourier coefficients for the initial state is also discussed.
  • #1
Knight
6
0
There is an initial state Psi(x) =Ax(b/2 - x) when 0< x <b/2 and Psi(x) = 0 when b/2 < x <b

I have to find the second lowest value possibly be obtained in a measurement of the energy.

Should I treat this as a box with width b and possible energy states E=n^2*h^2/8mb^2 ? Or should I use the width b/2 ?

Could someone please help me?
 
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  • #2
How are you going to incorporate the wave equations?
 
  • #3
Let me explain this problem better.
What I have to do is calculate the propability that the measured energy from this system is E2
O.K. So I have to find the Fourier coefficients, when I expand the initial state I mentioned above from 0 to b/2 in the eigenfunctions of the energy operator, or sqrt(2/b)*sin(n*pi*x/b). I know these eigenfunctions are derived from x=0 to x=b but Psi(x) =Ax(b/2 - x) is when 0< x <b/2
I am doing this the correct way or am I way off?
 
Last edited:

1. What is quantum chemistry?

Quantum chemistry is the branch of chemistry that studies the behavior of particles at the molecular and atomic levels using quantum mechanics principles.

2. What is the significance of quantum chemistry?

Quantum chemistry helps us understand the fundamental properties and behavior of matter at the atomic and molecular levels, which is crucial in fields such as materials science, drug discovery, and nanotechnology.

3. How is quantum chemistry different from classical chemistry?

Classical chemistry is based on classical mechanics, which describes the behavior of particles at the macroscopic scale. Quantum chemistry, on the other hand, uses quantum mechanics to explain the behavior of particles at the atomic and molecular scale.

4. What are some applications of quantum chemistry?

Quantum chemistry has various applications, including predicting molecular structures and properties, understanding chemical reactions, and designing new materials and drugs.

5. How does quantum chemistry contribute to the development of technology?

Quantum chemistry plays a crucial role in developing new technologies, such as quantum computing and quantum cryptography. It also helps in the development of new materials with unique properties for various applications.

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