filmov
tv
405 Bound Eigenstate Superposition Simulation Model
Показать описание
Quantum Mechanics: Bound Eigenstate Superposition Study GuideQuiz
Instructions: Answer each question in 2-3 sentences.
1. What are the fundamental building blocks of one-dimensional quantum mechanics, and how are they related?
2. What is the superposition principle in the context of quantum mechanics?
3. How are the expansion coefficients (cn) related in the wave function and what does this mean?
4. What determines the specific form of a wave function in this context?
5. What two types of eigenfunctions can be used to create a time-dependent wave function in the simulation described?
6. Why are atomic units used instead of the metric system when calculating quantum mechanics phenomena?
7. What are the atomic units of time, distance and energy in this model?
8. What is the significance of the time-independent Schrodinger equation in this simulation?
9. What software tool was used to develop the simulation and how can you further investigate it?
10. Besides the superposition principle, what other concepts does this simulation model?
Quiz Answer Key
1. The fundamental building blocks are energy eigenfunctions (ψn(x)) and energy eigenvalues (En). Eigenfunctions represent possible states of a system, while eigenvalues represent the corresponding energy levels.
2. The superposition principle states that a quantum-mechanical wave function (Ψ(x,t)) can be represented as a sum of energy eigenfunctions, each multiplied by an expansion coefficient (cn). This means that a particle can exist in multiple states simultaneously.
3. The expansion coefficients (cn) satisfy Σ c n|2 = 1. This ensures that the total probability of finding the particle in any of its possible states is 1.
4. The form of the wave function is determined by the potential energy function V ( x ) , boundary conditions, and the specific combination of the expansion coefficients. Different coefficients create energy eigenstates, superpositions, or localized wave packets.
5. The simulation uses either infinite square well (ISW) or simple harmonic oscillator (SHO) eigenfunctions to construct and display a time-dependent wave function. These represent the energy states in different models.
6. Metric units are not well suited because quantum phenomena occur on microscopic scales with very fast timescales making values too large or too small for computation. Using atomic units simplifies the calculations.
7. In this model, one unit time is 2.42×10-17 seconds, one unit of distance is 5.29×10-11 meters, and one unit of energy is 4.36×10-18 Joules.
8. The time-independent Schrödinger equation determines the energy eigenfunctions and eigenvalues for a given potential, enabling the calculation of possible particle states within the simulation's system.
9. The simulation was developed using the Easy Java/JavaScript Simulations (EjsS) modeling tool. You can examine and modify the simulation by importing the model's zip archive into EjsS if you have version 5.2 or higher.
10. Besides the superposition principle, this simulation also models infinite square well and simple harmonic oscillator potentials, and provides a way to study the time-dependent behavior of wave functions using these concepts.
Instructions: Answer each question in 2-3 sentences.
1. What are the fundamental building blocks of one-dimensional quantum mechanics, and how are they related?
2. What is the superposition principle in the context of quantum mechanics?
3. How are the expansion coefficients (cn) related in the wave function and what does this mean?
4. What determines the specific form of a wave function in this context?
5. What two types of eigenfunctions can be used to create a time-dependent wave function in the simulation described?
6. Why are atomic units used instead of the metric system when calculating quantum mechanics phenomena?
7. What are the atomic units of time, distance and energy in this model?
8. What is the significance of the time-independent Schrodinger equation in this simulation?
9. What software tool was used to develop the simulation and how can you further investigate it?
10. Besides the superposition principle, what other concepts does this simulation model?
Quiz Answer Key
1. The fundamental building blocks are energy eigenfunctions (ψn(x)) and energy eigenvalues (En). Eigenfunctions represent possible states of a system, while eigenvalues represent the corresponding energy levels.
2. The superposition principle states that a quantum-mechanical wave function (Ψ(x,t)) can be represented as a sum of energy eigenfunctions, each multiplied by an expansion coefficient (cn). This means that a particle can exist in multiple states simultaneously.
3. The expansion coefficients (cn) satisfy Σ c n|2 = 1. This ensures that the total probability of finding the particle in any of its possible states is 1.
4. The form of the wave function is determined by the potential energy function V ( x ) , boundary conditions, and the specific combination of the expansion coefficients. Different coefficients create energy eigenstates, superpositions, or localized wave packets.
5. The simulation uses either infinite square well (ISW) or simple harmonic oscillator (SHO) eigenfunctions to construct and display a time-dependent wave function. These represent the energy states in different models.
6. Metric units are not well suited because quantum phenomena occur on microscopic scales with very fast timescales making values too large or too small for computation. Using atomic units simplifies the calculations.
7. In this model, one unit time is 2.42×10-17 seconds, one unit of distance is 5.29×10-11 meters, and one unit of energy is 4.36×10-18 Joules.
8. The time-independent Schrödinger equation determines the energy eigenfunctions and eigenvalues for a given potential, enabling the calculation of possible particle states within the simulation's system.
9. The simulation was developed using the Easy Java/JavaScript Simulations (EjsS) modeling tool. You can examine and modify the simulation by importing the model's zip archive into EjsS if you have version 5.2 or higher.
10. Besides the superposition principle, this simulation also models infinite square well and simple harmonic oscillator potentials, and provides a way to study the time-dependent behavior of wave functions using these concepts.
0:15:56
0:00:41
0:55:06