How Can Quantum Mechanics Constants Be Deduced from Average Energy?

In summary, the conversation discusses a normalized wave function with constants representing ground and first excited states, and the average energy of the system. The particle is in a one dimensional well and the wave function is a linear combination of states. The coefficients must sum to 1 and the product of coefficients and eigenenergies must equal the total energy.
  • #1
greisen
76
0
Hey,

I have a normalized wave function

PSI = c_1 psi_1(x) + c_2 psi_1(x)

where c_1 and c_2 are constants with the eigenfunctions equal to ground and first excited state. The average energy of the system is pi^2hbar^2/(ma^2) - what can one deduce about the constant and how?

Thanks in advance
 
Physics news on Phys.org
  • #2
greisen said:
Hey,

I have a normalized wave function

PSI = c_1 psi_1(x) + c_2 psi_1(x)

where c_1 and c_2 are constants with the eigenfunctions equal to ground and first excited state. The average energy of the system is pi^2hbar^2/(ma^2) - what can one deduce about the constant and how?

Thanks in advance

I'm thinking energy expectation value, similar to your problem on creation/anihiliation. What are the eigenenergies of the two states?
 
  • #3
The particle is in a one dimensional well with V(x) = 0 for o <= x <= a and otherwise it is infinity. Is it a linear combination between the two states ?

Again thanks very much
 
  • #4
greisen said:
The particle is in a one dimensional well with V(x) = 0 for o <= x <= a and otherwise it is infinity. Is it a linear combination between the two states ?

Again thanks very much
Yes it is a linear combination of states. With orthonormal basis functions and normalized PSI the sum of the squares of the coefficients has to be 1. The products of coefficients times eigenenergies has to be the total energy
 

FAQ: How Can Quantum Mechanics Constants Be Deduced from Average Energy?

What are QM constants?

QM constants, or quantum mechanics constants, are numerical values used in quantum mechanics equations and models to describe the behavior of particles and systems at the atomic and subatomic level. These constants are fundamental in understanding the principles and laws of quantum mechanics.

What is the relationship between QM constants and average energy?

In quantum mechanics, the average energy of a system can be calculated using the QM constants, specifically the Planck constant and the frequency of the system. The Planck constant is used to determine the energy of a single quantum of a system, and the frequency is used to calculate the total energy of the system. Therefore, QM constants play a crucial role in determining the average energy of a quantum system.

How are QM constants determined?

QM constants are determined through experimental measurements and theoretical calculations. The values of these constants are derived from various physical phenomena, such as the energy levels of atoms and the behavior of particles in different systems. Over time, these values have been refined and standardized through repeated experiments and consensus among scientists.

What are some examples of QM constants?

Some examples of QM constants include the Planck constant, the speed of light, the electron charge, and the mass of an electron. These constants are used in a variety of equations and models in quantum mechanics, such as the Schrödinger equation and the Heisenberg uncertainty principle. Other examples include the Rydberg constant, the Avogadro constant, and the Boltzmann constant.

Why are QM constants important in scientific research?

QM constants are essential in scientific research because they provide a framework for understanding the behavior of particles and systems at the atomic and subatomic level. They allow scientists to make accurate predictions and calculations in quantum mechanics, which is crucial in fields such as chemistry, physics, and materials science. QM constants also help to bridge the gap between classical and quantum physics, providing a deeper understanding of the universe and its fundamental building blocks.

Similar threads

Can You Set Energy Conditions in Zwienbach Exercise 6.2?
Replies
10
Views
1K
Probability of finding a particle in the right half of a rectangular potential well
Replies
16
Views
2K
How Does Superposition Affect Measurements in a 1-D Harmonic Oscillator?
Replies
1
Views
2K
Is Every Linear Function a Linear Combination of Basis Functions?
Replies
2
Views
2K
Maximum position expectation value for 1D harmonic oscillator
Replies
12
Views
4K
Most Probable energy after infinite square well expands
Replies
2
Views
775
Quantum Mechanics determining the normalized constant of a particle
Replies
2
Views
1K
Average Kinetic Energy of Electron in the Conduction Band
Replies
4
Views
1K
Why Must the State of a Quantum SHM Particle Be of This Form?
Replies
6
Views
4K
Average value of the impulse as the parameters vary
Replies
14
Views
2K

Hot Threads

Recent Insights

Back
Top