Wave Mechanics Quiz

False (B)

The velocity at which the envelope of a group of waves travels.

<p>group velocity</p> Signup and view all the answers

<p>Phase velocity = Speed of a wave's phase Group velocity = Speed of the wave packet Wavelength = Distance between consecutive peaks Frequency = Number of cycles per second</p> Signup and view all the answers

<p>In dispersive media (D)</p> Signup and view all the answers

<p>True (A)</p> Signup and view all the answers

<p>Group velocity can depend on dispersion; in dispersive media, group velocity varies with frequency.</p> Signup and view all the answers

<p>$V ightarrow 0$ (B)</p> Signup and view all the answers

<p>False (B)</p> Signup and view all the answers

<p>y(x) = Bsin(kx)</p> Signup and view all the answers

<p>sqrt(2mE)</p> Signup and view all the answers

<p>n=1 = y(x) = sin(1x) n=2 = y(x) = sin(2x)</p> Signup and view all the answers

<p>y(x) = sin(1x) (A)</p> Signup and view all the answers

<p>True (A)</p> Signup and view all the answers

<p>y(0) = 0 and y(L) = 0</p> Signup and view all the answers

<p>The particle has uncertainties both in position and momentum. (B)</p> Signup and view all the answers

<p>True (A)</p> Signup and view all the answers

<p>Eigenfunctions maintain their form when acted upon by the operator.</p> Signup and view all the answers

<p>reduced</p> Signup and view all the answers

<p>Normalized wave function = Integral equals 1 Eigen function = Characteristic equation Cyclic coordinate = Does not appear in Lagrangian Degree of freedom = Independent motions of a system</p> Signup and view all the answers

<p>$\int \psi^* \psi ,dx = 1$ (D)</p> Signup and view all the answers

<p>False (B)</p> Signup and view all the answers

<p>The Lagrangian is a function of generalized coordinates and velocities. (D)</p> Signup and view all the answers

The average value of the position of a particle in a given state, calculated by integrating the product of the wavefunction, the position operator, and the complex conjugate of the wavefunction over all space.

The average value of the momentum of a particle in a given state, calculated by integrating the product of the wavefunction, the momentum operator, and the complex conjugate of the wavefunction over all space.

A mathematical equation that describes how the wavefunction of a quantum system evolves over time.

A simplified version of the Schrödinger's equation applied to a particle that does not experience any potential energy.

A mathematical equation that describes the stationary states of a quantum system, meaning states that do not change over time.

A simplified version of the time-independent Schrödinger's equation applied to a particle that does not experience any potential energy.

The Schrödinger's equation applied to a system that experiences potential energy.

The Schrödinger's equation extended to describe systems in three-dimensional space.

The total energy of a particle is equal to its kinetic energy since its potential energy is zero.

The time-independent Schrödinger equation for a particle in a box, where the potential energy is constant.

The general solution to the time-independent Schrödinger equation for a particle in a box, where A and B are arbitrary constants.

The boundary conditions imposed on the wave function to ensure it is physically realistic.

The process of determining the values of the constants A and B in the wave function using the boundary conditions.

The normalized wave function for a particle in a box, where the probability of finding the particle within the box is equal to one.

The eigenfunctions representing different energy states of a particle in a box.

The process of calculating the expectation value of an observable, such as position or momentum, for a given state of the particle in a box.

A wave function that describes the probability of finding a particle at a given position. In this context, the particle has a definite momentum but uncertainty in position. This means we know the particle's momentum, but we can't predict its exact location.

A type of coordinate used to represent a system's motion. It's independent of any specific reference frame and simplifies describing complex movements.

A coordinate in a Lagrangian system that doesn't appear explicitly in the Lagrangian. This makes it easier to simplify the system's description by ignoring the coordinate.

The number of independent parameters that are needed to completely describe the state of a system. In this case, the system has six independent parameters or degrees of freedom.

A function that, when acted upon by an operator, returns a multiple of itself. This multiple is called the eigenvalue, and the function is called an eigenfunction. The eigenfunction remains unchanged except for a scaling factor after the application of the operator.

The process of normalizing a wave function by ensuring that the probability of finding the particle in all possible locations adds up to 1. In this context, the normalization condition is that the integral of the squared magnitude of the wave function is equal to 1.

The average value of a quantity, like position or momentum, calculated using the wave function and the corresponding operator. This tells us the most likely value of the quantity we're measuring.

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