Eigenvalue Question (p2.14 in Quantum Chemistry and Spectroscopy)

In summary, an eigenvalue in quantum chemistry and spectroscopy is a characteristic value that describes the energy levels of a quantum system. It is used to determine energy levels and transitions, and is essential for understanding the electronic structure and properties of quantum systems. Eigenvalues are closely related to eigenvectors, with the former indicating energy levels and the latter representing the spatial distribution of the wavefunction. These eigenvalues can be experimentally determined through spectroscopic techniques.
  • #1
anduril66
2
0
function: e^-(x^2/2)
operator: d^2/dx^2 -x^2

The answer key says the function is an eigenfunction of the operator with an eigenvalue of -6.

I can't figure out how to reach this conclusion. Also, Wolfram Alpha says d/dx(d/(dx)e^(-x^2/2)) = e^(-x^2/2) (x^2-1). Isn't this inconsistent with the answer key? Thanks.
 
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  • #2
It is an eigenfunction, but with different eigenvalue.

ehild
 
  • #3
guys please help me doing this,
the operator is given as x+ d/dx
i have to find the eigenvalue. how to do it?
 

Related to Eigenvalue Question (p2.14 in Quantum Chemistry and Spectroscopy)

1. What is an eigenvalue in quantum chemistry and spectroscopy?

An eigenvalue in quantum chemistry and spectroscopy refers to a characteristic value that describes the energy levels of a quantum system. It is obtained by solving the Schrödinger equation for a given system and represents the possible energy values that a system can have.

2. How are eigenvalues used in quantum chemistry and spectroscopy?

Eigenvalues are used to determine the energy levels and corresponding wavefunctions of a quantum system. They are also used to calculate the transition energies and intensities in spectroscopic techniques such as infrared and nuclear magnetic resonance (NMR) spectroscopy.

3. What is the significance of eigenvalues in quantum chemistry and spectroscopy?

The eigenvalues of a quantum system provide important information about the energy states and transitions within the system. They are essential for understanding the electronic structure and properties of atoms, molecules, and other quantum systems.

4. How are eigenvalues related to eigenvectors?

Eigenvalues and eigenvectors are closely related in quantum chemistry and spectroscopy. An eigenvector is a mathematical vector that corresponds to a specific eigenvalue, and together they represent a state of the quantum system. The eigenvectors give information about the spatial distribution of the wavefunction, while the eigenvalues indicate the energy levels.

5. Can the eigenvalues of a quantum system be experimentally determined?

Yes, the eigenvalues of a quantum system can be experimentally determined through spectroscopic techniques such as absorption, emission, or scattering. By measuring the energy of the absorbed or emitted radiation, the transition energies and corresponding eigenvalues can be determined.

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