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.

we have been given a quadratic function and we need to restrict the domain such that it becomes a one to one function.

we know that vertex of this quadratic function occurs at (5,2).

further, we know that range of this function is .

if we restrict the domain of this function to either or , it will become one to one function.

let us know find its inverse.

upon interchanging x and y, we get:

let us now solve this function for y.

hence, the inverse function would be if we restrict the domain of original function to and the inverse function would be if we restrict the domain to .

it's when something is going so fast it makes a loud noise, breaking the sound barrier, for example: a jet makes a loud noise, not only cause of the jet but because they reached a point where they went so fast that you can year the noise from various parts, kinda like a police car, lets say the car was going   so fast that you hear the siren of the cop car right next to you, but the car is probably a mile a way, it's cos the siren was next to you a few seconds if you understand me

elctricity and magnet is conversion to it