But because there is the uncertainty principle in quantum mechanics , the particle ' s momenta and coordinates ca n ' t be determined at the same time , we ca n ' t use the orbits in phase space to describe quantum chaos 但是在量子力学中，由于不确定关系，粒子的动量和坐标不能同时被确定，所以经典庞加莱截面取法就不适用了。
Concept of knowledge in post modern times is the logic of humanistic thinking and conforms to uncertainty principle in quantum mechanics , " multi - value logic " in logistics and orientation in scientific hermeneutics 后现代知识观是一种人文思维的逻辑，它与量子力学的测不准原理、逻辑学中的“多值逻辑”以及科学解释理论中的转向有其一致性。
Quantum computing turns to its own advantage some of the apparent limitations that quantum physics imposes on the atomic world ? where heisenberg ' s uncertainty principle rules and particles behave in unpredictable ways 在处理一些利用量子力学研究原子时凸现出的瓶颈问题上?海森伯格不确定性原则在预测粒子运动上的矛盾?量子计算技术有着很多优势。
Quantum key distribution is based on the heisenberg ' s uncertainty principle which guarantees that no eavesdropper can escaped detection . a linchpin technology of quantum key distribution is single photon which is foundation of security 根据量子力学中的海森伯不确定性原理及未知单光子态不可克隆原理，任何窃听者无法窃听量子密码通信中的信息而不被发现。
Quantum communication is based on the quantum mechanics and cryptography , its security is guaranteed by the basic quantum principle - hersenberg ' s uncertainty principle and the quantum noncloning principle . so it is highlighted by people more and more 量子保密通信是密码学和量子力学相结合的产物，它的安全性由量子力学基本原理? ?测不准原理和单量子态不可克隆定理所保证，因而越来越受到人们的重视。
Only quantum mechanics can provide the answer : the particle ' s position will have an uncertainty that follows the heisenberg uncertainty principle , such that it might not really reach the singularity and thus escape the possible collapse to infinite density 只有量子力学可以提供答案：粒子的位置将具有不确定性，它们遵守海森堡测不准原理，因而它可能不是真的达到奇异而因此逃逸了可能的坍塌达到无限密度。
Quantum cryptography ( qc ) is the combination of classical cryptography and quantum mechanics . the characteristics of quantum mechanics , such as no - cloning theorem and heisenberg ' s uncertainty principle , provide the perfect secrecy for quantum cryptographic communication 量子密码学是密码学与量子力学结合的产物,利用量子不可克隆定理和海森堡测不准原理等量子特性，量子密码通信理论上已经证明是绝对安全。
So in normal atoms with electrons in stationary states , the probability of the electron being within the nucleus ( or somewhere else in atom within similarly small volume ) is nearly zero according to the uncertainty principle ( it is nearly zero as the nucleus has a volume and is not a point ) 因此在正常具有电子的原子里处于稳定状态，电子在核内的概率(或者处于原子里的某处类似小体积)是几乎为零按照测不准原理(它几乎为零如同核子具有体积而不是零那样) 。
One is the non - orthogonal gabor - daubechies frame , or g - d frame , a complete set of discrete window fourier functions which are constructed by space - shifting and harmonically modulating a gaussian window . although a g - d frame is not an orthogonal basis , it bears considerable advantages for the study of physical problems , especially those related to the wave field extrapolation , due to the optimal localization properties of the gaussian window function under the heisenberg uncertainty principle 其一为将高斯窗函数经平移和调制而构成的一组窗口富里叶框架( gabor - daubechies框架，或g - d框架)基本函数，另一种为在富里叶分析和小波包理论基础上发展起来的局部余弦基函数。
The termless security of quantum cryptographic key protocol is based on the quantum non - clone principle and heisenberg uncertainty principle . whilst , these two characteristics mentioned above contributes greatly to solve the problems of low transmitting rate , complicated operation and forge - identity assault in the bb84 protocol 量子密钥协议的无条件安全性能主要建立在量子不可克隆定理和heisenberg的测不准原理两大理论基础上的，但也正是由于量子的这两种特性导致在bb84协议中存在了传输效率低下、操作复杂、假冒身份攻击等方面的问题。
