What is Quantum mechanics: Definition and 995 Discussions
Quantum mechanics is a fundamental theory in physics that provides a description of the physical properties of nature at the scale of atoms and subatomic particles. It is the foundation of all quantum physics including quantum chemistry, quantum field theory, quantum technology, and quantum information science.
Classical physics, the description of physics that existed before the theory of relativity and quantum mechanics, describes many aspects of nature at an ordinary (macroscopic) scale, while quantum mechanics explains the aspects of nature at small (atomic and subatomic) scales, for which classical mechanics is insufficient. Most theories in classical physics can be derived from quantum mechanics as an approximation valid at large (macroscopic) scale.Quantum mechanics differs from classical physics in that energy, momentum, angular momentum, and other quantities of a bound system are restricted to discrete values (quantization), objects have characteristics of both particles and waves (wave-particle duality), and there are limits to how accurately the value of a physical quantity can be predicted prior to its measurement, given a complete set of initial conditions (the uncertainty principle).
Quantum mechanics arose gradually from theories to explain observations which could not be reconciled with classical physics, such as Max Planck's solution in 1900 to the black-body radiation problem, and the correspondence between energy and frequency in Albert Einstein's 1905 paper which explained the photoelectric effect. These early attempts to understand microscopic phenomena, now known as the "old quantum theory", led to the full development of quantum mechanics in the mid-1920s by Niels Bohr, Erwin Schrödinger, Werner Heisenberg, Max Born and others. The modern theory is formulated in various specially developed mathematical formalisms. In one of them, a mathematical entity called the wave function provides information, in the form of probability amplitudes, about what measurements of a particle's energy, momentum, and other physical properties may yield.
I'm currently self-studying quantum mechanics and instead of starting a new thread every time I have a new question I figure I'd just make one thread dedicated to all of them.
I'm going over the Photoelectric Effect. The way I understand it is when light is shone on a metallic surface, the...
Homework Statement
Demonstrate that the expectation value of momentum (p) for the wave function: ψ(x)∝e^(-γx) when x>0, ψ(x)=0 when x<0. Hint: Pay special attention to the discontinuity at x=0.[/B]
Homework Equations
<p>=<ψ|p|ψ>=∫dxψ*(x)[-iħ∂/∂x]ψ(x) from -∞ to ∞. [/B]The Attempt at a...
Homework Statement
"Show that the Slater Determinant states are a complete basis" is the entire statement.
Homework EquationsThe Attempt at a Solution
I guess I'm trying to prove that the rank of the states is equal to the basis? I'm not sure where to start on this one.
Homework Statement
A particle of mass m in the one-dimensional harmonic oscillator is in a state for which a measurement of the energy yields the values ##\hbar\omega/2## or ##3\hbar\omega/2## each with a probability of one-hald. The average value of the momentum ##\langle p_x\rangle## at...
Hello,
I have a conceptual problem. How can both General Relativity and a theory of Quantum Gravity simultaneously exist? GR describes gravity as the curvature of spacetime, while QG is most likely a gauge theory. Furthermore, if gravity is indeed describedby particle interactions-what does...
Homework Statement
Consider a particle in an energy eigenstate ##|n\rangle.##
Calculate ##\langle x\rangle## and ##\langle p_x\rangle## for this state.
Homework Equations
##x = \sqrt{\frac{\hbar}{2m\omega}}(a+a^{\dagger})##
The Attempt at a Solution
##\langle x\rangle =...
Why do Complex Numbers arise in Quantum Mechanics' computations? What kind of physical significance do they carry?
Someone told me to read this paper:
W E Baylis, J Hushilt, and Jiansu Wei, Why i?, American Journal of Physics 60 (1992), no. 9, 788–797.
But I found it difficult for me to...
I do not understand a work example in the book: ‘Quantum Mechanics DeMystified”.
On page 212, part of Example 7-5:
Given: Let { |a> |b> } be an orthonormal two-dimensional basis
Let Operator A be given by:
A = |a>< a |- i| a><b |+ i| b><a |- |b><b |
Then: (The following part I do not...
THE “INTELLIGENCE” BEHIND QUANTUM PHYSICS
If the nature of quantum mechanics is that an observer affects the end “collapsed” state of a particle, than what constitutes a state of observation. The the only thing I can come up with that seems to determine what constitutes a form of observation is...
I know that nuclear engineering requires some quantum mechanics but I want to know how much. Are there any textbooks that can fulfill the requirements for quantum mechanics in terms of nuclear engineering? I have heard of this book and I am a fan of old fashioned...
Hi, I've been self studying physics for a few years and I'm looking for some new books, specifically on Quantum Mechanics or Quantum Chemistry. It doesn't matter if they are PDF files or actual books, and price doesn't really matter. I've read Feynmans Lectures books and I'm looking for the next...
In many textbooks, the non-commutativity for the canonical pair is considered to lead to the major variaty from classical mechanism(CM) to quantum mechanism(QM), and change the Possion bracket into quantum commutator is a standard procedure called as canonical quantization. But in fact the...
I have just started reading about a classical electromagnetic treatment of light-matter interaction (beginning with dispersion relations, and then moving on to the standard phenomena - reflection, refraction, etc.). The discussion begins with a forewarning that light is not 'continuous' as the...
Homework Statement
Normalize the wave function $$ \langle x|\psi\rangle = \left\{ \begin{array}{l l} Ne^{-kx} & \quad x>0\\
Ne^{kx} & \quad x<0 \end{array} \right..$$
Determine the probability that a measurement of the momentum p finds the momentum between ##p## and ##p + dp## for this wave...
Homework Statement
I am currently working on a seemingly straightforward eigenvalue problem appearing as problem 1.8 in Sakurai's Modern QM. He asks us to find an eigenket \vert\vec S\cdot\hat n;+\rangle with \vec S\cdot\hat n\vert\vec S\cdot\hat n;+\rangle = \frac\hbar 2\vert\vec S\cdot\hat...
I have been looking online for books on introductory level quantum mechanics and General relativity that provide a mathematical introduction to these theories. Most of the books I have read until now provide a laymans introduction to these things.
Since I'm only pursuing this as a hobby and...
Hey I'm new to this forum and I'm 14 and I want to be a future Physicist (Probably Particle Physicist ) and I was wondering what books are good for starting out , just to let you know what kind of content I'm looking for I already know about General relativity , special relatativity , and the...
Hi, I know this is a basic question however, I am seeking absolute verification on these two points.
1) Quantum Mechanics is a set of Laws.
2) Laws only describe what we see. Theories give us the reason behind them.
Homework Statement
Let ##\langle\psi| = \int^{\infty}_{-\infty}dx\langle\psi|x\rangle\langle x|.## How do I calculate ##\langle\psi|\psi\rangle?##
Homework Equations
##\int^{\infty}_{-\infty}dxf(x)\delta(x-x_0)=f(x_0)##
The Attempt at a Solution
##\langle\psi|\psi\rangle = \int\int...
According to laplace,universe is totally deterministic.(one can tell position of object future position of object if he knows current position and velocity)but Heisenbergs's tells us that there is always uncertainty in position of particle and velocity.but Heisenberg's uncertainty only applies...
Homework Statement
The wave function of a certain particle is Ψ= A cos^2(x) for -π/2 < x < π/2. Find the value of A. Homework EquationsThe Attempt at a Solution
My answer is coming out to be zero wheres as the correct answer is under root 8/3π ... Please help me out !
I have often heard that in quantum mechanics time has no direction. That the physics works the same going backwards in time than forwards. How does the wave function collapse of a particle follow this idea? If we could see time go backwards would we see particles turning back into waves? Is...
Homework Statement [/B]
Just trying to find the spin 3/2 rotation matrix, I've found spin 1/2 and spin 1. This isn't a homework problem just studying some other spins.
Homework Equations
For spin 1/2: Rn(Φ) = cos(Φ/2)1ˆ − isin(Φ/2)σn
For spin 1: Un(Φ) = e −iΦSn = 1ˆ − isin(Φ) · Sn − (1ˆ −...
Homework Statement
Consider the Hamiltonian:
$$\hat{H}=C*(\vec{B} \cdot \vec{S})$$
where $C$ is a constant and the magnetic field is given by
$$\vec{B} = (0,B,0) $$
and the spin is
$$\vec{S} = (\hat{S}_{x},\hat{S}_{y},\hat{S}_{z}),$$
with$$\hat{S}_{x}...
Homework Statement
Particle of mass [tex[m[/tex] is confined on the ring of constant radius r_0. Solve Schroedinger equation for this problem.
Homework EquationsThe Attempt at a Solution
Problem is solved here
http://www.physics.oregonstate.edu/~corinne/COURSES/ph426/notes3.pdf
Why...
I'm learning about the Schrödinger equation in one of my uni courses, and we've recently gone past how to solve the time-independent version. That got me wondering if there is a space-independent version of the Schrödinger equation and what it could possibly be used for. I know I'm probably...
Most probably, there was already a thread about this before, but I didn't find any with the search engine. Please, believe me, I tried a lot of words and found nothing like I'm going to ask now.
I'm not a physicist...in fact, I'm a Political Sciences student with a great passion for Philosophy...
Hello!
If we consider a single-particle system, I understand that the measurement of an observable on this system will collapse the wave function of the system onto an eigenstate of the (observable) operator.
Therefore, we know the state of the system immediately after the measurement. But as...
Homework Statement
How can I find the matrix representation of ##\mathbb{S}_+## and ##\mathbb{S}_-## in the ##|\pm y\rangle## or ##|\pm x\rangle## basis?Homework Equations
##
\mathbb{\hat{S}}_+|s,m\rangle = \sqrt{s(s+1)-m(m+1)}\hbar|s,m+1\rangle
##
The Attempt at a Solution
The book almost...
Homework Statement
When calculating expectation values for spin states I encountered ##\langle \hat{\mathbb{S}}_+\rangle = \langle+z|\hat{\mathbb{S}}_+|+z\rangle = \frac12\langle+z|\hat{\mathbb{S}}_++\hat{\mathbb{S}}_-|+z\rangle.##
How do we compute...
Homework Statement
Use the spin##-1## states ##|1,1\rangle, \ |1,0\rangle, \ |1, -1\rangle## as a basis to form the matrix representations of the angular momentum operators. Homework Equations
##\mathbb{\hat{S}}_+|s,m\rangle = \sqrt{s(s+1)-m(m+1)}\hbar|s,m+1\rangle##...
Homework Statement
I am trying to find the possible measurement results if a measurement of a given observable ##Q=I-\left|u\right\rangle\left\langle u\right|## is made on a system described by the density operator ##\rho={1 \over 4}\left|u\right\rangle\left\langle u\right|+{3 \over...
Suppose we have a spin##-1## particle in a certain state ##|\phi\rangle## under the ##S_z## basis. How do you find the probabilities that a measurement of ##S_z## will result in the values of ##\hbar,0,## or ##-\hbar##?
Also, what does it mean exactly when it says what is the probability that...
Homework Statement
Show that for hydrogen the matrix element <2 0 0|z|2 1 0> = -3a0 where a0 is the Bohr Radius.
On account of the non-zero value of this matrix element, when an electric field is applied to a hydrogen
atom in its first excited state, the atom's energy is linear in the field...
Homework Statement
Determine the eigenstates of ##\hat{\mathbb{S}}_x## for a spin##-1## particle in terms of the eigenstates ##|1,1\rangle, \ |1,0\rangle,## and ##|1,-1\rangle## of ##\hat{\mathbb{S}}_z.##Homework EquationsThe Attempt at a Solution
Not sure exactly how to set this problem...
When trying to solve ##\mathbb{S}^2 =\hbar^2s(s+1)\mathbb{I},##
I got that ##\mathbb{S}^2 = \mathbb{S}^2 _x+\mathbb{S}^2_y+\mathbb{S}^2_z = \frac{3\hbar^2}{4}
\left[\begin{array}{ c c }1 & 0\\0 & 1\end{array} \right] = \frac{3\hbar^2}{4}\mathbb{I},## but how does ##\frac{3\hbar^2}{4} =...
Homework Statement
Calculate ##\triangle S_x## and ##\triangle S_y## for an eigenstate of ##\hat{S}_z## for a spin##-\frac12## particle. Check to see if the uncertainty relation ##\triangle S_x\triangle S_y\ge \hbar|\langle S_z\rangle|/2## is satisfied.
Homework Equations
##S_x =\frac12(S_+...
From Wiki:
"...the possible states of a quantum mechanical system are represented by unit vectors (called state vectors). Formally, these reside in a complex separable Hilbert space—variously called the state space or the associated Hilbert space of the system—that is well defined up to a...
I am trying to find the basic list of postulates that lay the foundation for QM, but i see a different list of postulates in different textbooks and different places.
In MIT lectures, Prof Allan Adams gives 3 basic postulates: 1. State of a system given by Wave function. 2. Mod squared psi gives...
Homework Statement
Prove that
## [L_a,L_b] = i \hbar \epsilon_{abc} L_c ##
using Einstein summation convention.
I think I have achieved the solution but I am not sure of my last steps, since this is one of my first excersises using this convention.
Homework Equations
[/B]
## (1)...
An article in Wikipedia tries to explain pigments.
One particular section has the following:
"A wide variety of wavelengths (colors) encounter a pigment. This pigment absorbs red and green light, but reflects blue, creating the color blue."
Questions arise... They may see stupid, but please...