Lecture 1

    Cards (168)

    • What are the key characteristics of the 2N3904 transistor?
      • Small signal amplifier
      • Maximum collector current (I_C): 200 mA
      • Maximum collector-emitter voltage (V_CE): 40 V
      • Maximum base-emitter voltage (V_BE): 5 V
      • Low power dissipation
    • What are the two assessment methods for PH284?
      1st Attempt (Exemption):
      • 20% Continuous assessment (CA)
      • 40% Semester 1 test
      • 40% Semester 2 test

      1st Attempt (Exam):
      • 80% Two-hour April/May exam
      • 20% Continuous assessment (CA)

      2nd Attempt:
      • 100% August two-hour exam
    • What is the primary content of the QP Syllabus?
      Introduction to quantum effects, De Broglie waves and uncertainty, Infinite potential well, Potential steps, barriers, tunnelling, Quantum harmonic oscillator, and quantum mechanics in 2D and 3D
    • What are Rayleigh-Jeans and Wien’s radiation laws?
      Rayleigh-Jeans Law:
      dnλ=dn_\lambda =(8πλ4)dλ (8 \pi \lambda^{-4}) \, d\lambda
      Uλ(T)=U_\lambda(T) =8πkTλ4 8 \pi kT \lambda^{-4}
      • Predicts ultraviolet catastrophe at short wavelengths
      • Works well for long wavelengths

      Wien’s Radiation Law:
      Uλ(T)=U_\lambda(T) =Aλ5eB/(λT) A \lambda^{-5} e^{-B/(\lambda T)}
      • Empirical with experimentally determined constants A and B
      • Works well for short wavelengths
      • Fails at long wavelengths
    • How does the spectral radiance change as the temperature increases?
      • The spectral radiance increases at all wavelengths
      • The peak radiance shifts to shorter wavelengths (Wien's displacement law)
      • The total power radiated increases (Stefan-Boltzmann law)
    • How does the experimental setup work for two-photon quantum imaging?
      1. A UV source emits position-correlated entangled photon pairs
      2. One photon passes through the object to be imaged
      3. The second photon is detected by a detector (e.g., bucket detector)
      4. The detected photon's position provides information about the first photon's path
      5. The first photon's path through the object is used to construct the image
    • What is the formula for the Compton shift?
      λλ=\lambda' - \lambda =λC(1cos(θ)) \lambda_C (1 - \cos(\theta))
    • What is the role of the second photon in two-photon quantum imaging?
      It acts as a signal to determine the first photon's path and contributes to image construction
    • What type of detector is commonly used to detect the second photon in two-photon quantum imaging?
      Bucket detector
    • Why might the class details and timetable be available via a link instead of directly on the study material?
      To provide the most current and easily accessible information
    • How did Planck derive his radiation law and what assumptions did he make?
      Planck’s Derivation:
      • Planck thought of radiation as a series of oscillators.
      • He assumed each oscillator’s energy was quantized in units of E=E =hf h f
      • This led to:
      Uλ=U_\lambda =8πhcλ5ehc/(λkT)1 \frac{8 \pi h c \lambda^{-5}}{e^{hc/(\lambda k T)} - 1}
      • h=h =6.63×1034J.s 6.63 \times 10^{-34} \, \text{J.s} is Planck’s constant and k=k =1.38×1023J K1 1.38 \times 10^{-23} \, \text{J K}^{-1} is Boltzmann’s constant.

      Einstein’s contribution:
      • Einstein added physical rigour to Planck’s assumption.
      • He showed each oscillator’s energy must be quantized as En=E_n =nhf, n h f, where n is an integer.
    • What happens to the wavelength of maximum energy density as a body is heated?
      The wavelength of maximum energy density reduces.
    • What is Wien’s displacement law formula?
      λmaxT=\lambda_{max} T =2.90×103 m K 2.90 \times 10^{-3} \text{ m K}
    • What type of scientific instrument is shown in the image?
      • A high-vacuum apparatus
      • Typically used for surface science experiments
    • Why is high vacuum important in such instruments?
      It minimizes collisions with the sample, ensuring a clean surface
    • What type of bits are used in quantum computers?
      Quantum bits (qubits).
    • What are the main components and roles in the tutorials?
      • Tutorials support lectures and practice problem solving.
      • One hour per week.
      • Mix of individual (7.5%) and group (7.5%) problems.
      • In the first week, students pick groups of 5 on MyPlace.
      • Each two-week block allocates a group problem and 4 individual MyPlace questions.
      • Weeks 1-3, 5, 7, 9 are for working through group problems.
      • Weeks 4, 6, 8, 10 are for groups to present solutions.
      • Groups can use Onedrive Documents for collaborative editing.
      • Roles include presenter, solver, scribe, and checker.
      • Group assembly and presentation of worked solutions enhance skills.
    • What were some key observations that challenged classical physics?
      • The elements: Why are there ~100 elements and how do they form a periodic table?
      • Blackbody radiation: Experimental spectra did not match theoretical models.
      • Photoelectric effect: Experimental observations disagreed with classical predictions.
      • Compton effect: X-rays scattered off crystals changed their wavelength unexpectedly.
      • Atomic structure: Unclear about atoms ‘inside’ and why light from atomic vapour lamps was at discrete colours.
    • How is the Stefan-Boltzmann law derived from Planck’s law?
      By integrating Planck's law
    • What can be measured in a photoelectric effect experiment?
      • The photocurrent as a function of applied voltage.
    • What is the formula for the momentum of a photon?
      p=p =hλ \frac{h}{\lambda}
    • What is the formula for the angular momentum of an electron according to Bohr?
      L=L =mevr= m_e v r =n n \hbar
    • What is the vector form of de Broglie’s equation?
      p=p =k \hbar \vec{k}
    • What is the formula for the de Broglie wavelength of an electron in terms of accelerating voltage?
      λ=\lambda =h2mqV \frac{h}{\sqrt{2 m q V}}
    • What was observed about the scattering pattern of electrons?
      Electrons were scattered strongly in one direction
    • What generates the electron beam?
      • Electron gun (heated wire)
    • How does the extra distance travelled by the electron beam parts relate to the lattice spacing?
      2l = 2d sin(φ)
    • What mathematical tools are used to describe matter waves in Quantum Physics?
      • Wavefunctions
      • Schrödinger equation
      • Complex numbers
      • Partial differential calculus
    • What is the product of z1=z_1 =13i 1 - 3i and the complex conjugate of z2=z_2 =3+ -3 +4i? 4i?
      • 15 + 5i
    • What is the condition for constructive interference?
      2d sin(φ) = n λ for integer n
    • Find the derivative of f(x)=f(x) =tan(x). \tan(x).
      sec<sup>2</sup>(x)
    • Find the partial derivative fy\frac{\partial f}{\partial y} of f(x,y)=f(x, y) =sin(πx+2πy). \sin(\pi x + 2\pi y).
      2πcos(πx+2πy)2\pi \cos(\pi x + 2\pi y)
    • What are the two standard forms of harmonic wave functions?
      • ψ(x,t)=\psi(x, t) =Asin(kxωt)+ A \sin(kx - \omega t) +Bcos(kxωt) B \cos(kx - \omega t)
      • Aei(kxωt)A e^{i(kx - \omega t)}
    • How does the Born interpretation relate the wave function to the probability of finding a particle?
      • The square of the amplitude of the wave function (ψ2)(|\psi|^2) gives the probability density
      • Integrating this over a region gives the probability of finding the particle in that region
    • Write the general form of a harmonic wave function.
      ψ(x,t)=\psi(x, t) =Aei(kxωt) A e^{i(kx - \omega t)}
    • Express z=z =5eiarctan(4/3) 5 e^{-i \arctan(4/3)} in Cartesian form.

      3 - 4i
    • Why is f(x)=f'(x) =sec2(x) \sec^2(x) true for f(x)=f(x) =tan(x)? \tan(x)?
      Using the product rule and trigonometric identities
    • What is the formula for the allowed energies of a Hydrogenic atom according to Bohr?
      En=E_n =Z2e28πϵ0a0n2= -\frac{Z^2 e^2}{8\pi \epsilon_0 a_0 n^2} =Z2×13.6 eVn2 -\frac{Z^2 \times 13.6 \text{ eV}}{n^2}
    • What mathematical tools are used to describe matter waves in Quantum Physics?
      • Wavefunctions
      • Schrödinger equation
      • Complex numbers
      • Partial differential calculus
    • What type of image is produced in two-photon quantum imaging?
      Upright image
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