Problem 2 please explain. problem 3 problem In any physical system, there are ob

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Problem 2 please explain.

problem 3 problem

In any physical system, there are observable quantities. For a baseball in projectile motion, some of these include the kinetic energy, height above the ground, momentum, and angle. In quantum mechanics, we use operators to measure the observable quantities. Every observable quantity in a quantum-mechanical system has a corresponding operator that is used to measure the observable. For example, the momentum of the system corresponds to the result of the momentum operator, x= - d/dz The position operator is x = x. The operators are applied to the eigenfunction solutions of Schrodinger's equation, or linear combinations of the eigenfunctions, and return real-number eigenvalues of the operator. This average measurement (a) is called the expectation value of a. In general, does (x)2 equal (x2 )? Explain your answer.Particle in a 3-D Box: Counting States Problems that require solving the three-dimensional Schrodinger equation can often be reduced to related one-dimensional problems. An example of this would be the particle in a cubical box. Consider a cubical box with rigid walls (i.e., U(x, y, z) = infinity outside of the cube) and edges of length L The general solution for this problem is where nx, ny, and nz are all positive integers. Note that this solution is just the product of three solutions to the one-dimensional particle in a box. The energy corresponding to the three-dimensional solution is just the sum of the energies for each of the three one-dimensional solutions: When using quantum mechanics to describre large collections of particles, such as the electrons in a piece of metal, it is important to know how many quantum states exist below a certain energy. For the three-dimensional box potential, there is a convenient graphical way to do this. Since there are three different quantum numbers (nx, ny, and nz), picture three-dimensional space with each number measured down one of the axes. (Figure 1) The energy is proportional to the sum of the squares of the three numbers, which corresponds to the distance from the origin squared. To ask how many states have energy less than or equal to some number Part B If you are dealing with a very large nrs, you can assume that each state (point with integer coordinates) corresponds roughly to one unit of volume inside of the sphere. So, the number of states is approximately equal to the volume of the octant of the sphere. Use this idea to find the number N of states with energy less than or equal to

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for the question requiring you to drag and place answers into the sentences: Does not, Average, Average, cannot. Those are correct based on mastering chem.

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