Consider a novel harmonic oscillator in which the hamiltonian operator takes the form where α and at satisfy the anti-commutation relations: use these anti-commutation relations to show the following: (a) show that h2 hh. what are the possible eigenvalues of h? hint: there are two eigenvalues. (5 points) (b) show that there must be a state annihilated by å. call this state po, such that αφο-0. (3 points) (c) show that φο cannot be annihilated by à, ie, that àtqbo 0. let φ1 ξ àton (3 points) (d) show that àol-фо, and àtdy-0. (3 points) (3 points) (f) suppose an electron is in the infinite potential well with length l. the electron is only allowed to be in the ground state, or the first excited state. if we want to use the ladder operators a and a to describe our system and write its hamiltonian as eq. (1), what should be the value of hw? (3 points) hint: the eigen-energy of electron in infinite potential wel for the n-th eigen- state: en-npr2h2/(2ml? )

quantum mechanics or quantum physics is physics of very small objects (particles) and physical entities.

quantum physics has some parallels to our macro world and some pretty unique ideas which theoretically and mathematically proven to be true even though we will never be able to access them because of our size.

there are many types of particles: subatomic, elementary etc.

subatomic means they are smaller than atom, elementary means they are at the very basis of everything.

subatomic particles are for eg. protons, neutrons but not electrons.

elementary particles are categorised into 3 groups by what they do.

these 3 groups are quarks, leptons and bosons.

light for example is a particle more precisely a photon a part of leptons.

proton (subatomic particle) is made out of 2 up quarks and 1 down quark each of these has a fractional charge like . (i crazy)

most famous scientist who contributed to this physics are:

the topic itself us understand a lot and will probably be vastly used in the future (quantum computers, understanding the big bang,

we also must not forget quantum effects like:

and there is more. but probably too much for this answer to be consistent due to my average understanding of this topic.

hope this you understand quantum mechanics a little more. i'm not an expert in the topic (so don't be like wth if you are an expert) but i'm very interested in it.

anyways quantum physics is a very hard topic (harder than physics (perhaps)) therefore searching for every information there is about it and learning it is unfortunately impossible (you can only specialise into 1 - 3 things or more (perhaps

have fun and i wish you luck!

r3t40

when a device is used in a circuit in which the voltage is 81 v, the current flowing through the device is 3 a. what is the resistance of the device?

a. 27 ω

b. 40.5 a

c. 243 ω

d. 243 a

the correct answer is a. 27

it would be c. predictability

get the total number of pieces of fruit and divide it by 4 to get the average. the result is the answer to the problem. 14 total number of fruits and there are 4 members. 14 divided by 4 is equals to 3.5.