Show that the wavefunction y = eikx + e-ikx is an eigenfunction of the hamiltonian operator for a free particle (for which potential energy, v, = 0 everywhere). normalization of wavefunctions 3. consider the function from question 1 (e-ax). based on the condition that wavefunctions of physical systems must be normalizable, is this an acceptable wavefunction? 4. find the normalization factor for the wavefunction y(x) = eix for x = -0.5 to 0.5. 5. let's suppose i confine the particle i'm interested in to x values between zero and some distance a. (meaning that the particle must exist somewhere between 0 and a.) find the normalization factor and write out the normalized wavefunctionf for: w(x) = sin (ex); where a is a constant note: totally fine with me if you use something like wolframalpha to evaluate this, but if you do, screenshot your input and result to submit to me.

Apossible explanation for a set of facts that can be tested by further investigation is called

Kate is working on a project in her tech education class. she plans to assemble a fan motor. which form of energy does the motor convert most of its electric energy into? a. light energy b. motion energy c. sound energy d. thermal energy

The frequency of vibrations of a vibrating violin string is given by f = 1 2l t ρ where l is the length of the string, t is its tension, and ρ is its linear density.† (a) find the rate of change of the frequency with respect to the following. (i) the length (when t and ρ are constant) (ii) the tension (when l and ρ are constant) (iii) the linear density (when l and t are constant) (b) the pitch of a note (how high or low the note sounds) is determined by the frequency f. (the higher the frequency, the higher the pitch.) use the signs of the derivatives in part (a) to determine what happens to the pitch of a note for the following. (i) when the effective length of a string is decreased by placing a finger on the string so a shorter portion of the string vibrates df dl 0 and l is ⇒ f is ⇒ (ii) when the tension is increased by turning a tuning peg df dt 0 and t is ⇒ f is ⇒ (iii) when the linear density is increased by switching to another string df dρ 0 and ρ is ⇒ f is ⇒