0
Everything you've ever wanted to know can be found at the link below.
Wiki User
∙ 13y ago
Add your answer:
Earn +20 pts
What is normalising a wave function?
A wave function is normalized by determining normalization constants such that both the value and first derivatives of each segment of the wave function match at their intersections. If instead you meant renormalization, that is a different problem having to do with elimination of infinities in certain wave functions.
Why do you normalise a wave function of a particle?
There are two parts to this. First is, "What is the physical significance of a wave function?" Secondly, "Why do we normalize it?"To address the first:In the Wave Formulation of quantum mechanics the wave function describes the state of a system by way of probabilities. Within a wave function all 'knowable' (observable) information is contained, (e.g. position (x), momentum (p), energy (E), ...). Connected to each observable there is a corresponding operator [for momentum: p=-i(hbar)(d/dx)]. When the operator operates onto the wave function it extracts the desired information from it. This information is called the eigenvalue of the observable... This can get lengthy so I'll just leave it there. For more information I suggest reading David Griffith's "Introduction to Quantum Mechanics". A math knowledge of Calculus II should suffice.To address the second:Normalization is simply a tool such that since the probability of finding a particle in the range of +/- (infinity) is 100% then by normalizing the wave function we get rid of the terms that muddy up the answer the probability.An un-normalized wave function is perfectly fine. It has only been adopted by convention to normalize a wave function.ex. un-normalized wave function (psi is defined as my wave function)- The integral from minus infinity to positive infinity of |psi|^2 dx = 2piex. normalized wavefunction- The integral from minus infinity to positive infinity of |psi|^2 dx = 1
Physical significance of green function in quantum mechanics?
There are two parts to this. First is, "What is the physical significance of a wave function?" Secondly, "Why do we normalize it?"To address the first:In the Wave Formulation of quantum mechanics the wave function describes the state of a system by way of probabilities. Within a wave function all 'knowable' (observable) information is contained, (e.g. position (x), momentum (p), energy (E), ...). Connected to each observable there is a corresponding operator [for momentum: p=-i(hbar)(d/dx)]. When the operator operates onto the wave function it extracts the desired information from it. This information is called the eigenvalue of the observable... This can get lengthy so I'll just leave it there. For more information I suggest reading David Griffith's "Introduction to Quantum Mechanics". A math knowledge of Calculus II should suffice.To address the second:Normalization is simply a tool such that since the probability of finding a particle in the range of +/- (infinity) is 100% then by normalizing the wave function we get rid of the terms that muddy up the answer the probability.An un-normalized wave function is perfectly fine. It has only been adopted by convention to normalize a wave function.ex. un-normalized wave function (psi is defined as my wave function)- The integral from minus infinity to positive infinity of |psi|^2 dx = 2piex. normalized wavefunction- The integral from minus infinity to positive infinity of |psi|^2 dx = 1
What are orthogonal wave functions?
Math Prelude: Orthogonal wave functions arise as a natural consequence of the mathematical structure of quantum mechanics and the relevant mathematical structure is called a Hilbert Space. Within this infinite dimensional (Hilbert) vector space is a definition of orthogonal that is exactly the same as "perpendicular" and that is the natural generalization of "perpendicular" vectors in ordinary three dimensional space. Within that context, wave functions are orthogonal or perpendicular when the "dot product" is zero. Quantum Answer: With that prelude, we can then say that mathematically, the collection of all quantum states of a quantum system defines a Hilbert Space. Two quantum functions in the space are said to be orthogonal when they are perpendicular and perpendicular means the "dot product" is zero. Physics Answer: The question asked has been answered, but what has not been answered (because it was not was not asked), is why orthogonal wave functions are important. As it turns out, anything that you can observe or measure about the state of a quantum system will be mathematically represented with Hermitian operators. A "pure" state, i.e. one where the same measurement always results in the same answers, is necessarily an eigenstate of a Hermtian operator and any two pure states that give two different results of measurement are necessarily "orthogonal wave functions." Conclusion: Thus, there are infinitely many orthogonal wave functions in the set of all wave functions of a quantum system and that orthogonal property has no physical meaning. When one identifies the subset of quantum states that associated pure quantum states (meaning specifically measured properties) and then two distinguishable measurement outcomes are associated with two different quantum states and those two are orthogonal. But, what was asked was a question of mathematics. Mathematically orthogonal wave functions do not guarantee distinct pure quantum state, but distinct pure quantum states does guarantee mathematically orthogonal wave functions. You can remember that in case someone asks.
Why the wave function must be normalized?
It has to do with probabilities. The area under the curve of a wavefunction can be whatever you want it to be. You normalize the curve to have the total probability equal to 1, which makes the mathematics a lot easier. We do this with statistics and probabilities all the time.
What is normalising a wave function?
A wave function is normalized by determining normalization constants such that both the value and first derivatives of each segment of the wave function match at their intersections. If instead you meant renormalization, that is a different problem having to do with elimination of infinities in certain wave functions.
Why do you normalise a wave function of a particle?
There are two parts to this. First is, "What is the physical significance of a wave function?" Secondly, "Why do we normalize it?"To address the first:In the Wave Formulation of quantum mechanics the wave function describes the state of a system by way of probabilities. Within a wave function all 'knowable' (observable) information is contained, (e.g. position (x), momentum (p), energy (E), ...). Connected to each observable there is a corresponding operator [for momentum: p=-i(hbar)(d/dx)]. When the operator operates onto the wave function it extracts the desired information from it. This information is called the eigenvalue of the observable... This can get lengthy so I'll just leave it there. For more information I suggest reading David Griffith's "Introduction to Quantum Mechanics". A math knowledge of Calculus II should suffice.To address the second:Normalization is simply a tool such that since the probability of finding a particle in the range of +/- (infinity) is 100% then by normalizing the wave function we get rid of the terms that muddy up the answer the probability.An un-normalized wave function is perfectly fine. It has only been adopted by convention to normalize a wave function.ex. un-normalized wave function (psi is defined as my wave function)- The integral from minus infinity to positive infinity of |psi|^2 dx = 2piex. normalized wavefunction- The integral from minus infinity to positive infinity of |psi|^2 dx = 1
Physical significance of green function in quantum mechanics?
There are two parts to this. First is, "What is the physical significance of a wave function?" Secondly, "Why do we normalize it?"To address the first:In the Wave Formulation of quantum mechanics the wave function describes the state of a system by way of probabilities. Within a wave function all 'knowable' (observable) information is contained, (e.g. position (x), momentum (p), energy (E), ...). Connected to each observable there is a corresponding operator [for momentum: p=-i(hbar)(d/dx)]. When the operator operates onto the wave function it extracts the desired information from it. This information is called the eigenvalue of the observable... This can get lengthy so I'll just leave it there. For more information I suggest reading David Griffith's "Introduction to Quantum Mechanics". A math knowledge of Calculus II should suffice.To address the second:Normalization is simply a tool such that since the probability of finding a particle in the range of +/- (infinity) is 100% then by normalizing the wave function we get rid of the terms that muddy up the answer the probability.An un-normalized wave function is perfectly fine. It has only been adopted by convention to normalize a wave function.ex. un-normalized wave function (psi is defined as my wave function)- The integral from minus infinity to positive infinity of |psi|^2 dx = 2piex. normalized wavefunction- The integral from minus infinity to positive infinity of |psi|^2 dx = 1
What are orthogonal wave functions?
Math Prelude: Orthogonal wave functions arise as a natural consequence of the mathematical structure of quantum mechanics and the relevant mathematical structure is called a Hilbert Space. Within this infinite dimensional (Hilbert) vector space is a definition of orthogonal that is exactly the same as "perpendicular" and that is the natural generalization of "perpendicular" vectors in ordinary three dimensional space. Within that context, wave functions are orthogonal or perpendicular when the "dot product" is zero. Quantum Answer: With that prelude, we can then say that mathematically, the collection of all quantum states of a quantum system defines a Hilbert Space. Two quantum functions in the space are said to be orthogonal when they are perpendicular and perpendicular means the "dot product" is zero. Physics Answer: The question asked has been answered, but what has not been answered (because it was not was not asked), is why orthogonal wave functions are important. As it turns out, anything that you can observe or measure about the state of a quantum system will be mathematically represented with Hermitian operators. A "pure" state, i.e. one where the same measurement always results in the same answers, is necessarily an eigenstate of a Hermtian operator and any two pure states that give two different results of measurement are necessarily "orthogonal wave functions." Conclusion: Thus, there are infinitely many orthogonal wave functions in the set of all wave functions of a quantum system and that orthogonal property has no physical meaning. When one identifies the subset of quantum states that associated pure quantum states (meaning specifically measured properties) and then two distinguishable measurement outcomes are associated with two different quantum states and those two are orthogonal. But, what was asked was a question of mathematics. Mathematically orthogonal wave functions do not guarantee distinct pure quantum state, but distinct pure quantum states does guarantee mathematically orthogonal wave functions. You can remember that in case someone asks.
Why the wave function must be normalized?
It has to do with probabilities. The area under the curve of a wavefunction can be whatever you want it to be. You normalize the curve to have the total probability equal to 1, which makes the mathematics a lot easier. We do this with statistics and probabilities all the time.
How is a sine curve related to a wave?
See the link belowA sine wave is computed by a mathematical function. A pure sine wave in a physical sense would exactly match the calculated value in the function at every point in time.
what is wave function?
The official definition for the word wave function is "a function that satisfies a wave equation and describes the properties of a wave."
How will you calculate potential if the wave function is given?
Square the wave function.
What is sinc function?
In mathematics and engineering, the sinc function, denoted by sinc(x), has two slightly different definitions.[1]In mathematics, the historical unnormalized sinc functionis defined byIn digital signal processing and information theory, the normalized sinc function is commonly defined by The normalized sinc (blue) and unnormalized sinc function (red) shown on the same scale.
What are the Differentiate the sine wave and cosine wave?
The differential of the sine function is the cosine function while the differential of the cosine function is the negative of the sine function.
What is the definition of orthogonal signal space?
Orthogonal signal space is defined as the set of orthogonal functions, which are complete. In orthogonal vector space any vector can be represented by orthogonal vectors provided they are complete.Thus, in similar manner any signal can be represented by a set of orthogonal functions which are complete.
Can the difference of 2 vectors be orthogonal?
The answer will depend on orthogonal to WHAT!
