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For the particle-in-a-box of length a, assume that instead of a sine function, the ground state wavefunction is an upside-down parabola at the center of the box, b/2. What is the total energy of...
Slaonu yoar mork - No wark Nocrslit- IFI cannot follanz the math- Na credlit Bonus Question: (20 pts) For the particle-in-a-box of length a, assume that instead of a sine function, the ground sta...
Slaonu yoar mork - No wark Nocrslit- IFI cannot follanz the math- Na credlit Bonus Question: (20 pts) For the particle-in-a-box of length a, assume that instead of a sine function, the ground state wavefunction is an upside-down parabola at the center of the box, b/2. What is the total energy of the trial system and what is the wavefunction of the system. Now compare your result to the particle-in-a-box where the potential energy inside the box is zero, what...
09 Estimate the ground state energy and wavefunction for a particle in a box using the...
09 Estimate the ground state energy and wavefunction for a particle in a box using the variational method with the following trial wavefunction, where N is the normalization constant and ß is a variational parameter that should be minimized. 14) = N exp(-Bx2) (7.6) 1. Is this a good trial wavefunction for this approximation (justify your answer)? 2. Why is this not a good wavefunction? 3. Can you solve this problem both analytically and numerically? Pay careful attention to limits...
Example To obtain the ground state energy of a particle in a one-dimensional box, a graduate...
Example To obtain the ground state energy of a particle in a one-dimensional box, a graduate student used a postulated wavefunction of the form Y = e-ax? where a is a variational parameter. Along the process, the student obtained the following result. ſy trial ÀY trial Etrial = There are trial trial Complete the variation calculation procedure and obtain the optimal value of a.
If a particle is in a box with a ground state energy of 4 eV, what...
If a particle is in a box with a ground state energy of 4 eV, what energy must be absorbed by the system to go from the n = 2 state to the n = 3 state?
4. A (one dimensional) particle in a box of length 2a (i.e., zero potential energy) is...
4. A (one dimensional) particle in a box of length 2a (i.e., zero potential energy) is represented by the wavefunction v(x) 0, otherwise a. Sketch the wavefunction. Write down the (time independent) Schrodinger equation. Show whether or not the wavefunction is a solution to the equation. b. What does it mean physically if the wavefunction of the particle is NOT a solution to the Schrodinger equation? Explain. c. Determine the normalization constant A. 5. Same system. Find the average or...
For the one-dimensional particle in a box of length L = 1 Å, what will be...
For the one-dimensional particle in a box of length L = 1 Å, what will be the energy of the ground state? a. Write Schrodinger’s equation for if the potential between 0 and L is zero b. Write Schrodinger’s equation for if the potential between 0 and L has a constant value of V_o
6. The Particle in a Box problem refers to a potential energy function called the infinite square...
6. The Particle in a Box problem refers to a potential energy function called the infinite square well, aka the box: ; x < 0 (Region I) V(x) = 0 : 0 L (Region II) x x >L (Region III) Let's investigate a quantum particle with mass m and energy E in this potential well of length L We were unable to transcribe this image6d (continued) write down an equation relating ψ, (x = 0) to ψ"(x I and II....
8.4 The Two-Dimensional Central-Force Problem The 2D harmonic oscillator is a 2D central force pr...
8.4 The Two-Dimensional Central-Force Problem The 2D harmonic oscillator is a 2D central force problem (as discussed in TZD Many physical systems involve a particle that moves under the influence of a central force; that is, a force that always points exactly toward, or away from, a force center O. In classical mechanics a famous example of a central force is the force of the sun on a planet. In atomic physics the most obvious example is the hydrogen atom,...
Question 1 1 pts What is the kinetic energy of a man who weighs 980N who...
Question 1 1 pts What is the kinetic energy of a man who weighs 980N who is riding in a car traveling 40 km per hour? Express your answer in Joules, but don't type the unit in the answer box. Round to the nearest whole number. (Careful with the units) 1 pts Astudent slides her 80.0-kg desk across the level floor of her dormitory room a distance 4.00 m at constant speed. If the coefficient of kinetic friction between the...
Clearly state your solution path. Partial credit will only be given for clear steps. Units must...
Clearly state your solution path. Partial credit will only be given for clear steps. Units must be provided or points will be subtracted. Clearly label the end result, use double lines to underscore or box the final result. Note the equation sheet is on the back. (10 pt) An electron enters a region between two capacitor plates with equal and opposite charges. The plates are L=0.1 m by 0.05 m and the gap between the plates is h=0.001 m. During...
Slaonu yoar mork - No wark Nocrslit- IFI cannot follanz the math- Na credlit Bonus Question: (20 pts) For the particle-in-a-box of length a, assume that instead of a sine function, the ground state wavefunction is an upside-down parabola at the center of the box, b/2. What is the total energy of the trial system and what is the wavefunction of the system. Now compare your result to the particle-in-a-box where the potential energy inside the box is zero, what...
09 Estimate the ground state energy and wavefunction for a particle in a box using the variational method with the following trial wavefunction, where N is the normalization constant and ß is a variational parameter that should be minimized. 14) = N exp(-Bx2) (7.6) 1. Is this a good trial wavefunction for this approximation (justify your answer)? 2. Why is this not a good wavefunction? 3. Can you solve this problem both analytically and numerically? Pay careful attention to limits...
Example To obtain the ground state energy of a particle in a one-dimensional box, a graduate student used a postulated wavefunction of the form Y = e-ax? where a is a variational parameter. Along the process, the student obtained the following result. ſy trial ÀY trial Etrial = There are trial trial Complete the variation calculation procedure and obtain the optimal value of a.
4. A (one dimensional) particle in a box of length 2a (i.e., zero potential energy) is represented by the wavefunction v(x) 0, otherwise a. Sketch the wavefunction. Write down the (time independent) Schrodinger equation. Show whether or not the wavefunction is a solution to the equation. b. What does it mean physically if the wavefunction of the particle is NOT a solution to the Schrodinger equation? Explain. c. Determine the normalization constant A. 5. Same system. Find the average or...
6. The Particle in a Box problem refers to a potential energy function called the infinite square well, aka the box: ; x < 0 (Region I) V(x) = 0 : 0 L (Region II) x x >L (Region III) Let's investigate a quantum particle with mass m and energy E in this potential well of length L We were unable to transcribe this image6d (continued) write down an equation relating ψ, (x = 0) to ψ"(x I and II....
8.4 The Two-Dimensional Central-Force Problem The 2D harmonic oscillator is a 2D central force problem (as discussed in TZD Many physical systems involve a particle that moves under the influence of a central force; that is, a force that always points exactly toward, or away from, a force center O. In classical mechanics a famous example of a central force is the force of the sun on a planet. In atomic physics the most obvious example is the hydrogen atom,...
Question 1 1 pts What is the kinetic energy of a man who weighs 980N who is riding in a car traveling 40 km per hour? Express your answer in Joules, but don't type the unit in the answer box. Round to the nearest whole number. (Careful with the units) 1 pts Astudent slides her 80.0-kg desk across the level floor of her dormitory room a distance 4.00 m at constant speed. If the coefficient of kinetic friction between the...
Clearly state your solution path. Partial credit will only be given for clear steps. Units must be provided or points will be subtracted. Clearly label the end result, use double lines to underscore or box the final result. Note the equation sheet is on the back. (10 pt) An electron enters a region between two capacitor plates with equal and opposite charges. The plates are L=0.1 m by 0.05 m and the gap between the plates is h=0.001 m. During...
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