Check to see whether the simple linear combination of sine and cosine functions

$$\psi=A \sin (k x)+B \cos (k x)$$

satisfies the time-independent Schrodinger equation for a free particle (V = 0).

An electron is trapped in an infinite square-well potential of width 0.70 nm. If the electron is initially in the (n=4) state, what are the various photon energies that can be emitted as the electron jumps to the ground state?

Determine the slope and the $y$-intercept of the line whose equation is given.

$$12x=6y+4$$

Find absolute value.

$$\mid 0 \mid$$

An electron microscope is designed to resolve objects as small as 0.14 nm. What energy electrons must be used in this instrument?

For the infinite square-well potential, find the probability that a particle in its ground state is in each third of the one-dimensional box: $0 \leq x \leq L / 3, L / 3 \leq x \leq 2L/3, 2 L / 3 \leq x \leq L$. Check to see that the sum of the probabilities is one.

Tell whether the statement is true or false. If it is false, explain why. Every function is a relation.

Write the point-slope form of the equation of the line satisfying each of the conditions. Then use the point-slope form of the equation. to write the slope-intercept form of the equation. Passing through ( - 2 , - 4 ) and ( 1 , - 1 )

There are 80 questions from an SAT test, and they are all multiple choice with possible answers of a, b, c, d, e. For each question, only one answer is correct. Find the mean and standard deviation for the numbers of correct answers for those who make random guesses for all 80 questions.

An electron moves with a speed $v=1.25 \times 10^{-4} c$ inside a one-dimensional box (V = 0) of length 48.5 nm. The potential is infinite elsewhere. The particle may not escape the box. What approximate quantum number does the electron have?

In what ways do human activities influence the nitrogen cycle?

Prove that for each positive integer n, there is a unique scalar matrix whose trace is a given constant k.

Express each number in decimal notation.

$$1.39x10^{-4}$$

A particle in an infinite square-well potential has ground-state energy 4.3 eV. (a) Calculate and sketch the energies of the next three levels, and (b) sketch the wave functions on top of the energy levels.