Module 1
Quantum Mechanics
Dr. F. Jyothi Serrao
Professor
Dept. of Physics. SCEM
BPH102GC/BPH202GC
Quantum mechanics is a fundamental branch of physics, developed in the early 20th century to
address the limitations of classical mechanics and to provide a comprehensive framework for
understanding the behaviour of matter and energy at the atomic and subatomic scales. A cornerstone
of Quantum Mechanics is the Heisenberg Uncertainty Principle. This principle has profound
implications, highlighting the inherent probabilistic nature of quantum systems. Quantum
Mechanics has successfully explained a wide array of phenomena that classical mechanics could
not, ranging from the stability of atoms to the properties of semiconductors. It forms the foundation
for modern technologies like lasers and transistors and continues to drive advancements in fields
such as quantum computing.
Stern–Gerlach Experiment: The Stern–Gerlach experiment, performed in 1922 by Otto Stern and
Walther Gerlach, demonstrated the quantized nature of angular momentum in atoms and ultimately
led to the discovery of the spin property of the electron.
In the experiment, silver was heated in an oven, and the silver atoms coming out were passed
through collimating slits to form a narrow beam. This beam was then passed through a non-uniform
magnetic field created between specially shaped north and south pole pieces. Each silver atom has
only one unpaired electron in its outer 5s orbital, and its orbital angular momentum is zero and
therefore its magnetic effect comes only from the intrinsic spin of the electron.
According to classical physics, the magnetic moments of atoms could be oriented in any direction,
so the beam of silver atoms after experiencing a force in the non-uniform magnetic field, would
produce a continuous distribution of spots on the photographic plate.
, However, the beam of silver atoms split into exactly two distinct parts, producing two well-
separated spots on the photographic plate. This result showed that the spin of the electron in silver
atoms can only take two discrete orientations along the chosen z-axis of the magnetic field,
1 1
corresponding to the spin quantum numbers 𝑚𝑠 =+ 𝑎𝑛𝑑 𝑚𝑠 =− . Thus, the Stern–Gerlach
2 2
experiment provided direct evidence for the quantization of angular momentum and proved the
existence of electron spin, a fundamental property of matter.
de Broglie’s concept of matter waves:
In 1924 Louis de Broglie proposed a concept called matter waves.
According to him, when a particle of mass ‘m’ moves with a velocity ‘v’, it exhibits a wave nature.
The wave associated with the moving particle is called a matter wave and its wavelength
(de-Broglie wavelength) is given as
h h
= = Where h Planks constant, p momentum
mv p
Characteristics of matter waves
ℎ
1) The wavelength of the matter wave is given by 𝜆= , it shows that lighter the particle, the
𝑚𝑣
greater is the wavelength associated with it.
2) If V= 0, then λ =∞, that means the matter waves are generated only by the moving particles.
3) Matter waves are not electromagnetic waves and can be associated with any particles whether
charged or uncharged
4) Matter waves can propagate in a vacuum; hence they are not mechanical waves.
5) Matter waves travel faster than light (Phase velocity is greater than the speed of light)
6) In matter waves, there is a periodic variable quantity called wave function (ψ). It is a measure
of the probability of finding the particle at a given position and time.
Heisenberg’s Uncertainty principle:
Statement: “It is impossible to determine both parameters of a conjugate pair (such as position and
momentum, or energy and time), simultaneously with complete accuracy, and the product of their
𝒉
uncertainties is always greater than or equal to “
𝟒𝝅
The most common conjugate pairs are
𝒉
• Position (x) and momentum (p), ∆𝒙. ∆𝒑 ≥
𝟒𝝅
2
Quantum Mechanics
Dr. F. Jyothi Serrao
Professor
Dept. of Physics. SCEM
BPH102GC/BPH202GC
Quantum mechanics is a fundamental branch of physics, developed in the early 20th century to
address the limitations of classical mechanics and to provide a comprehensive framework for
understanding the behaviour of matter and energy at the atomic and subatomic scales. A cornerstone
of Quantum Mechanics is the Heisenberg Uncertainty Principle. This principle has profound
implications, highlighting the inherent probabilistic nature of quantum systems. Quantum
Mechanics has successfully explained a wide array of phenomena that classical mechanics could
not, ranging from the stability of atoms to the properties of semiconductors. It forms the foundation
for modern technologies like lasers and transistors and continues to drive advancements in fields
such as quantum computing.
Stern–Gerlach Experiment: The Stern–Gerlach experiment, performed in 1922 by Otto Stern and
Walther Gerlach, demonstrated the quantized nature of angular momentum in atoms and ultimately
led to the discovery of the spin property of the electron.
In the experiment, silver was heated in an oven, and the silver atoms coming out were passed
through collimating slits to form a narrow beam. This beam was then passed through a non-uniform
magnetic field created between specially shaped north and south pole pieces. Each silver atom has
only one unpaired electron in its outer 5s orbital, and its orbital angular momentum is zero and
therefore its magnetic effect comes only from the intrinsic spin of the electron.
According to classical physics, the magnetic moments of atoms could be oriented in any direction,
so the beam of silver atoms after experiencing a force in the non-uniform magnetic field, would
produce a continuous distribution of spots on the photographic plate.
, However, the beam of silver atoms split into exactly two distinct parts, producing two well-
separated spots on the photographic plate. This result showed that the spin of the electron in silver
atoms can only take two discrete orientations along the chosen z-axis of the magnetic field,
1 1
corresponding to the spin quantum numbers 𝑚𝑠 =+ 𝑎𝑛𝑑 𝑚𝑠 =− . Thus, the Stern–Gerlach
2 2
experiment provided direct evidence for the quantization of angular momentum and proved the
existence of electron spin, a fundamental property of matter.
de Broglie’s concept of matter waves:
In 1924 Louis de Broglie proposed a concept called matter waves.
According to him, when a particle of mass ‘m’ moves with a velocity ‘v’, it exhibits a wave nature.
The wave associated with the moving particle is called a matter wave and its wavelength
(de-Broglie wavelength) is given as
h h
= = Where h Planks constant, p momentum
mv p
Characteristics of matter waves
ℎ
1) The wavelength of the matter wave is given by 𝜆= , it shows that lighter the particle, the
𝑚𝑣
greater is the wavelength associated with it.
2) If V= 0, then λ =∞, that means the matter waves are generated only by the moving particles.
3) Matter waves are not electromagnetic waves and can be associated with any particles whether
charged or uncharged
4) Matter waves can propagate in a vacuum; hence they are not mechanical waves.
5) Matter waves travel faster than light (Phase velocity is greater than the speed of light)
6) In matter waves, there is a periodic variable quantity called wave function (ψ). It is a measure
of the probability of finding the particle at a given position and time.
Heisenberg’s Uncertainty principle:
Statement: “It is impossible to determine both parameters of a conjugate pair (such as position and
momentum, or energy and time), simultaneously with complete accuracy, and the product of their
𝒉
uncertainties is always greater than or equal to “
𝟒𝝅
The most common conjugate pairs are
𝒉
• Position (x) and momentum (p), ∆𝒙. ∆𝒑 ≥
𝟒𝝅
2
