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Schrodinger Equation and Hydrogen Atom (Bohr’s model of the hydrogen atom) Schrodinger Equation: Well, Step, Barrier Part 3 Schrodinger Equation...

Schrodinger Equation and Hydrogen Atom (Bohr’s model of the hydrogen atom) Schrodinger Equation: Well, Step, Barrier Part 3 Schrodinger Equation Part 2 Electron microscopy Part 4 Heisenberg Uncertainty Relationships De Broglie’s Hypothesis Wave-Par(cle Duality Wave-like particle of electron Part 1 Concepts from Part 1 &2 1  1801: Young’s double-slit experiment: wave behavior of light through interference patterns. 1887: Hertz discovered that UV light can cause sparks between metal electrodes: a particle-like behavior of light. 1905: Following Hertz's discovery, Einstein explained the photoelectric effect and photons, contributing to the understanding of wave-particle duality of light. 1924: Broglie proposed the concept of wave-particle duality of matter : electrons have the wave-like behavior as shown in a de Broglie wavelength. 1926: Schrödinger formulated the Schrödinger Eq., highlighting the wave-like behavior of electrons through wave functions. 1927: Davisson and Germer showed that electrons are scattered by a crystal in their electron diffraction experiments, confirming a wave-like behavior of electrons. 1927: Heisenberg formulates the Uncertainty Principle, highlighting fundamental limits in measuring quantum systems, i.e. , position and momentum cannot be simultaneously measured with precision. 1950s: Electron microscopy utilizing the wave-like behavior of electrons was developed. 2 เกณฑ์ การให้ คะแนน 50% 20% - มีสว่ นร่วมในชันเรี + ยน (เช่น quiz ก่อนเรี ยน /ระหว่างเรี ยน) - การบ้ าน ไม่คดั ลอกมาจากเพื>อน – เขียน และ upload (pdf) ใน LEB2 ภายใน 1 สัปดาห์หลังจาก มอบหมายงาน 30 % (Final Exam) - ผิด-ถูก / ปรนัย/ อัตนัย - 90% ของข้ อสอบจะดัดแปลงมาจากในสไลด์ที>สอนในระดับความยาก-ง่ายที>ใกล้ เคียงกัน 10% ของข้ อสอบจะดัดแปลงมาจากเนื +อหาที>สอนแต่จะมีความยาก-ง่ายที>สงู กว่าโจทย์ตวั อย่าง 3 Part 1 4 Outline 1.1 Wave-Par+cle Duality 1.2 Uncertainty Rela+onships 1.3 Heisenberg Uncertainty Rela+onships 5 1.1 Wave-Particle Duality 6 1.1 Wave-Particle Duality èthe concept that light and electrons (including other quantum particles) can exhibit both wave-like and particle-like properties. (depending on the experimental setup) à The evidence for light behaving as wave: interference, diffraction, polarization, and reflection. à UV light could cause sparks to jump between metal electrodes. Einstein (1905) explained the effect and demonstrated the particle-like behavior of light. (Photoelectric effect) à X-rays were scattered by electrons in a material, the scattered X-rays exhibited a longer wavelength than the incident X-rays, indicating a transfer of energy and a loss of energy in the process. (Compton effect) à Electron appears as a localized point with mass and charge (classical particles). However, it can exhibit interference patterns (wave behavior) in double-slit experiment. à In classical, neutrons contribute to the mass and stability of atoms. However, it exhibits interference patterns in neutron diffraction experiments. 7 1.1 Wave-Particle Duality Photoelectric effect 5. The energy of a photon depends on its frequency (f). 1. A phenomenon in which electrons are emitted from a metal surface when it is exposed to light (photon) of enough frequency. ! = ℎ$ 2. Light is expressed in term of photon. h = Planck's equation 3. The emitted electron is called photoelectron. 6. Light intensity (I) is a measure of the number of photons per 4. This effect was first observed and explained by unit area and per unit (me. Einstein and is a fundamental principle in the field of quantum mechanics. 7. So, with a higher light intensity, there are more photons available to interact with the metal, leading to a larger number of photoelectrons being emiSed. Example, 8 1.1 Wave-Particle Duality Photoelectric effect - Escape the material entirely. - Free from the material’s potential. Vacuum level (eV) - Not the same for all metals; 1. Threshold frequency (!% ): (e.g., electronic structure, surface Solid-state physics conditions ) The minimum frequency of incident light (photon) required to initiate the emission of photoelectrons (A) CB from a metal surface. 2. Work func the highest energy level in a material at absolute zero temperature (0 K or -273.15°C) at which electrons can occupy. => It serves as a reference point in energy band theory for the distribution of electrons in a solid. => above absolute zero (0 K), the Fermi level indicates the energy state at which the probability of à Minimum amount of energy finding an electron is 50%. needed to remove an electron from the metal. In metals, work function and ionization energy are the same. 10 (h#ps://en.wikipedia.org/wiki/Fermi_level#/media/File:Band_filling_diagram.svg) 1.1 Wave-Particle Duality Photoelectric effect ⑰ & = ℎ# (1) ℎ# = % + &' (3) (energy of photon) (conservation of energy in fro + Ei photoelectric effect) ℎ#& = % (2) 1 (specific for each metal) !! = %& " (4) 2 (Here, it is a maximum value) 11 1.1 Wave-Particle Duality Final Photoelectric effect UV UV SEM oo ℎ$ = ( + ! (5) potenti ! ! = ℎ+ (1) 1 5678, 23 # = -.$%% (8) ℎ+# = , (2) & stopping 1 23 # = -." (6) 2 2 > → ( Wave-particle duality : particle-like behavior and wave-like behavior è something we know it’s there, but we cannot measure it simultaneously. è we cannot measure it as in the wave form in classical è we have to extract the information from ‘wave function (math func.)’ i.e. particle behavior: position (x), momentum (p) i.e., wave behavior: wavelength (!), frequency (f), amplitude (A), period (T) ==> So, if we can localize the wave to specific region, like wave packet, then we can describe the particle 1) Modulating function: such as gaussian Superimposing: wave function 2) Superimposing: larger number of these wave packet waves. Here, there is constructive interference in tiny region and destructive interference every where else. 33 1.2 Uncertainty Relationships Oconcept Amplitude For light (electromagnetic waves) -Wave: amplitude of the wave is related to the intensity or brightness of the light In quantum mechanics (wave-parAcle duality), light can behave as a parAcle like a photon. - we explain by using ‘wave funcJon’ - Wave funcAon: the amplitude of the wave funcJon is associated with probability. for example, the square of the amplitude of the wave funcAon gives the probability density of finding the parAcle (photon, electron, etc.) at a parAcular locaAon when measured. 34 1.2 Uncertainty Relationships In wave-par