# 客家科學精神與佛教思想研究

## 全文

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1.如果用波函數來描述粒子的運動行為,則一定無法同時準確的 描述粒子的位置及動量。

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(2) well-definedλ= 2π/k andυ=ω/2

(3) travels in “+x” direction , v =λ•υ=ω/ k →this particle:

(4) has a well-defined p= h/λ→動量的不確定性, Δpx = 0

(5) P( x,t ) dV = ∣Ψ∣2 dV = A2dV at any point ( Particle can

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(2) but narrower width of the resulting wave packet (3) consistent with uncertainty principle

Ψ ( x,t =0 )∣2

7.to describe a partially localized particle :

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greater range of k

→ greater range of λ (λ = 2π / k )

→ less well-defined momentum, Δ px ↑ ( px = h/λ ) → narrower width of the resulting wave packet

→ better localized particle , Δ x↓ → consistent with uncertainty principle

(二)、波包行進的速度 – 群速( Velocity of Wave Packet – Group Velocity )

1.group velocity → velocity of the particle

Ψ(x,t)=Ψ1+Ψ2

= Asin【（k+Δk）x-(ω+Δω)t】+Asin(kx-ω t)

sin a+ sin b=2cos(a-b)/2sin(a+b)/2

→Ψ(x,t)=2Acos( Δkx-Δωt )sin【(2k+Δk)x-（2 ω+Δω）t】

2 2 =2Acos(Δ kx-Δ ω t )sin(kx-ω t)

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The envelop travels at v group v group=Δ ω /2 = Δ ω /Δ k＝dω /dk Δ k/2 λ =h/p λ =2π /k → k = p / h → dk = dp / h υ =E/h υ =ω /2π → ω = E/ h → dω = dE / h →v group= dω / dk = dE / dp = d( p2 ) / dp 2m = 2p / 2m = m v particle / m = vparticle →vgroup = vparticle

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OR 波幅(wave magnitude)越大 →粒子出現的機率越大 1.物質波或粒子波所代表的是粒子出現機率的機率波( waves of probability ) 哥本哈根詮釋 Copenhagen Interpretation 2.wave magnitude→indication of the probability that the

particle will be found at that point 3.in particle model :

I ( intensity ) N , density of the particle in wave model :

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4.let the particle wave be represented by Ψ( r, t ) Ψ( r,t ) : wave function ( 波函數 ) ,r : position 5. The probability that the particle will be found in volume dV : P( r,t ) dV = ∣Ψ∣2 dV , P( r,t ) = ∣Ψ∣2 : probability density ∫∞ －∞ ∣Ψ∣2 dv =1 ( normalization ) 量子力學主要在幹什麼 ? →尋找或計算一個物理系統 ( 單粒子或多粒子系統 ) 的波 函數

6. 單電子發射的雙狹縫干涉實( double-slit experiment with series of

Single electron emissions )

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### 參考文獻

Dalai Lama (2005) The Universe in a Single Atom: The Convergence of Science and Spirituality, New York: The Broadway Books. Lopez, D. S., Jr. (2008) Buddhism and Science, Chicago: The

University of Chicago Press.

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