P2: Quantum Mechanics

Give the formula related to change in E

and h dash

and a approximation to plank’s constant

Give de Broglie relation and momentum formula

c=v x lambda, v (Hz/s-1) frequency

What is i and i²

what is a complex number z and its conjugate

i= square root (-1)

i²= (-1)

z = x+iy

its conjugate z* = x - iy

What is square modulus

and absolute value (modulus)

I𝑧I² =𝑧∗𝑧=𝑧𝑧∗ = (𝑥 +𝑖𝑦 )(x −𝑖𝑦)= 𝑥² +𝑦²

I𝑧I = square root(𝑧∗𝑧) = square root(𝑥² +𝑦²)

The equation 𝑥 +4 = 0

Has two solutions 𝑥 = 2𝑖 and 𝑥 = −2𝑖

Born Interpretation of the wavefunction?

What is Probability of finding a particle in region 0 ≤𝑥≤ 1 in a 1D box

What is the Probability of finding a particle in volume ?

What is the Probability of finding a particle anywhere in space?

Name all parts in the pic and

Let’s consider operator 𝐴 = dx/dy , and a function 𝑓 (𝑥) =12e ^-3x

f(x) is eigenfunction of 𝐴 with eigenvalue -3

𝑑𝑓/𝑑𝑥 =12× (−3)𝑒^−3× =(-3)f

What is The time-independent Schrödinger equation is an eigenproblem of the energy operator?

\what is the formula used for Calculating the quantum average?

Write down the formula for the Uncertainty principle

Give the Relation between potential energy and force in a harmonic oscillator

and its relation

V is potential E in J

kf force constant Nm-1

x in m, extension of the spring

give an approximation of with units:

Planck’s constant

speed of light in ms-1 and cm-1

what we use to convert miu → kg

h≈ 6.63×10^−34Js
c≈ 3.00×10^8 cm s−1

c≈ 3.00×10^10 cm s−1

1u≈ 1.66×10^−27kg

Write J in 4 different terms and N in kg

Kg m2 s-2

Nm-1

CV-1, V is (volts)

Ws-1

1N= 1Kgm-1s-2

C and V in terms of s

and what is the me ( e- mass)

and kinetic E formula

C ≡ A s

V ≡ kg m2 s −3 A −1

me≈9.11×10^−31 kg

Ek= 1/2(mv²)

How to convert wavenumber to frequency

and how c relates to wavelength

v=wavenumber x c

v=s-1 or Hz

c=cms-1

wavenumber = cm-1

c= v x lambda

how to turn v from cm-1 to J

how to turn energy per photon → energy per mole

what is 1pm

what is 1 Angstrom

E=hv

multiply by avogardo NA= 6.022×10^23mol−1

1pm= 10^-12m

1 angstrom = 10^-10m